|
Search: id:A035506
|
|
|
| A035506 |
|
Stolarsky array read by antidiagonals. |
|
+0
9
|
|
| 1, 2, 4, 3, 6, 7, 5, 10, 11, 9, 8, 16, 18, 15, 12, 13, 26, 29, 24, 19, 14, 21, 42, 47, 39, 31, 23, 17, 34, 68, 76, 63, 50, 37, 28, 20, 55, 110, 123, 102, 81, 60, 45, 32, 22, 89, 178, 199, 165, 131, 97, 73, 52, 36, 25, 144, 288, 322, 267, 212, 157, 118, 84, 58
(list; table; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Inverse of sequence A064357 considered as a permutation of the positive integers. - Howard A. Landman (howard(AT)polyamory.org), Sep 25 2001
GP-PARI program gives general solution for the Stolarsky array in square array form by row,column. Increase the default precision, if computing large values in the array. - Randall L. Rathbun (randallr(AT)abac.com), Jan 25 2002
|
|
REFERENCES
|
C. Kimberling, "Stolarsky interspersions," Ars Combinatoria 39 (1995) 129-138.
C. Kimberling, "Interspersions and dispersions," Proceedings of the American Mathematical Society 117 (1993) 313-321.
|
|
LINKS
|
C. Kimberling, Interspersions
N. J. A. Sloane, Classic Sequences
Eric Weisstein's World of Mathematics, Stolarsky arrays
Index entries for sequences that are permutations of the natural numbers
|
|
EXAMPLE
|
Top left corner of array is:
1 2 3 5 8 13...
4 6 10 16 26...
7 11 18 29 47...
9 15 24 39 63...
|
|
MAPLE
|
A := proc (n, k) local t, a, b; t:= (1+sqrt(5))/2; a:= floor (n*(1+t)-t/2); b:= round (a*t); (Matrix([[b, a]]). Matrix([[1, 1], [1, 0]])^(k-1))[1, 2] end: seq (seq (A (n, d-n), n=1..d-1), d=1..11); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 17 2008]
|
|
PROGRAM
|
(PARI) {Stolarsky(r, c)= tau=(1+sqrt(5))/2; a=floor(r*(1+tau)-tau/2); b=round(a*tau); if(c==1, a, if(c==2, b, for(i=1, c-2, d=a+b; a=b; b=d; ); d))}
|
|
CROSSREFS
|
Sequence in context: A083050 A083044 A126714 this_sequence A006016 A054239 A048680
Adjacent sequences: A035503 A035504 A035505 this_sequence A035507 A035508 A035509
|
|
KEYWORD
|
nonn,tabl,easy,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms from Larry Reeves (larryr(AT)acm.org), Sep 27 2000
|
|
|
Search completed in 0.003 seconds
|
