Search: id:A035513
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%I A035513
%S A035513 1,2,4,3,7,6,5,11,10,9,8,18,16,15,12,13,29,26,24,20,14,21,47,42,39,32,
%T A035513 23,17,34,76,68,63,52,37,28,19,55,123,110,102,84,60,45,31,22,89,199,
%U A035513 178,165,136,97,73,50,36,25,144,322,288,267,220,157,118,81,58,41,27
%N A035513 Wythoff array read by antidiagonals.
%C A035513 T(0,0)=1, T(0,1)=2,...; y^2-x^2-xy<y if and only if there exist (i,j) 
               with x=T(i,2j) and y=T(i,2j+1) - Claude Lenormand (claude.lenormand(AT)free.fr), 
               Mar 17 2001
%C A035513 Inverse of sequence A064274 considered as a permutation of the nonnegative 
               integers. - Howard A. Landman (howard(AT)polyamory.org), Sep 25 2001
%C A035513 The Wythoff array W consists of all the Wythoff pairs (x(n),y(n)), where 
               x=A000201 and y=A001950, so that W contains every positive integer 
               exactly once. The differences T(i,2j+1)-T(i,2j) form the Wythoff 
               difference array, A080164, which also contains every positive integer 
               exactly once. - Clark Kimberling (ck6(AT)evansville.edu), Feb 08 
               2003
%C A035513 For n>2 the determinant of any n X n contiguous subarray of A035513 (as 
               a square array) is 0. - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), 
               Sep 18 2004
%C A035513 Comments from Clark Kimberling (ck6(AT)evansville.edu), Nov 14 2007 (Start): 
               Except for initial terms in some cases:
%C A035513 (Row 1) = A000045
%C A035513 (Row 2) = A000032
%C A035513 (Row 3) = A006355
%C A035513 (Row 4) = A022086
%C A035513 (Row 5) = A022087
%C A035513 (Row 6) = A000285
%C A035513 (Row 7) = A022095
%C A035513 (Row 8) = A013655 (sum of Fibonacci and Lucas numbers)
%C A035513 (Row 9) = A022112
%C A035513 (Column 1) = A003622 = AA Wythoff sequence
%C A035513 (Column 2) = A035336 = BA Wythoff sequence
%C A035513 (Column 3) = A035337 = ABA Wythoff sequence
%C A035513 (Column 4) = A035338 = BBA Wythoff sequence (End)
%D A035513 C. Kimberling, "Stolarsky interspersions," Ars Combinatoria 39 (1995) 
               129-138.
%D A035513 C. Kimberling, The Zeckendorf array equals the Wythoff array, Fibonacci 
               Quarterly 33 (1995) 3-8.
%H A035513 Alois P. Heinz, <a href="b035513.txt">Table of n, a(n) for n = 1..5151</
               a>
%H A035513 C. Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/intersp.html">
               Interspersions</a>
%H A035513 N. J. A. Sloane, <a href="http://www.research.att.com/~njas/doc/sg.txt">
               My favorite integer sequences</a>, in Sequences and their Applications 
               (Proceedings of SETA '98).
%H A035513 N. J. A. Sloane, <a href="classic.html#WYTH">Classic Sequences</a>
%H A035513 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               WythoffArray.html">Wythoff Array</a>
%H A035513 <a href="Sindx_Per.html#IntegerPermutation">Index entries for sequences 
               that are permutations of the natural numbers</a>
%F A035513 T(n, k) = Fib(k+1)*floor[n*tau]+Fib(k)*(n-1) where tau = (sqrt(5)+1)/
               2 and Fib(n) = A000045(n). - Henry Bottomley (se16(AT)btinternet.com), 
               Dec 10 2001
%e A035513 The Wythoff array begins:
%e A035513 ...1....2....3....5....8...13...21...34...55...89..144 ...
%e A035513 ...4....7...11...18...29...47...76..123..199..322..521 ...
%e A035513 ...6...10...16...26...42...68..110..178..288..466..754 ...
%e A035513 ...9...15...24...39...63..102..165..267..432..699.1131 ...
%e A035513 ..12...20...32...52...84..136..220..356..576..932.1508 ...
%e A035513 ..14...23...37...60...97..157..254..411..665.1076.1741 ...
%e A035513 ..17...28...45...73..118..191..309..500..809.1309.2118 ...
%e A035513 ..19...31...50...81..131..212..343..555..898.1453.2351 ...
%e A035513 ..22...36...58...94..152..246..398..644.1042.1686.2728 ...
%e A035513 ..25...41...66..107..173..280..453..733.1186.1919.3105 ...
%e A035513 ..27...44...71..115..186..301..487..788.1275.2063.3338 ...
%e A035513 .......
%p A035513 W:= proc(n,k) Digits:= 100; (Matrix ([n, floor((1+sqrt(5))/2* (n+1))]). 
               Matrix([[0,1], [1,1]])^(k+1))[1,2] end: seq (seq (W(n, d-n), n=0..d), 
               d=0..10); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 18 
               2008]
%Y A035513 Cf. A003622. See also comments above.
%Y A035513 Sequence in context: A108228 A127008 A064274 this_sequence A114537 A021808 
               A105081
%Y A035513 Adjacent sequences: A035510 A035511 A035512 this_sequence A035514 A035515 
               A035516
%K A035513 nonn,tabl,easy,nice
%O A035513 1,2
%A A035513 N. J. A. Sloane (njas(AT)research.att.com).
%E A035513 More terms from James W. Scheid (s1147798(AT)cedarville.edu)

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