Search: id:A001592
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%I A001592 M1128 N0431
%S A001592 0,0,0,0,0,1,1,2,4,8,16,32,63,125,248,492,976,1936,3840,7617,15109,
%T A001592 29970,59448,117920,233904,463968,920319,1825529,3621088,7182728,
%U A001592 14247536,28261168,56058368,111196417,220567305,437513522,867844316
%N A001592 Hexanacci numbers: a(n+1)=a(n)+...+a(n-5).
%C A001592 a(n-5) is the number of ways of throwing n with an unstated number of 
               standard dice and so the row sum of A061676; for example a(9)=8 is 
               the number of ways of throwing a total of 4: 4, 3+1, 2+2, 1+3, 2+1+1, 
               1+2+1, 1+1+2 and 1+1+1+1; if order did not distinguish partitions 
               (i.e. the dice were indistinguishable) then this would produce A001402 
               instead. - Henry Bottomley (se16(AT)btinternet.com), Apr 01 2002
%C A001592 Number of permutations satisfying -k<=p(i)-i<=r, i=1..n-5, with k=1, 
               r=5. - Vladimir Baltic (baltic(AT)matf.bg.ac.yu), Jan 17 2005
%C A001592 a(n)=number of compositions of n-5 with no part greater than 6. Example: 
               a(12)=63 because we have 63 compositions of 7: 7=1+1+1+1+1+1+1=2+1+1+1+1+1=...=2+2+1+1+1=...=2+2+2+1=...=\
               3+1+1+1+1=... =3+2+1+1=...=3+2+2=...=3+3+1=...=4+1+1+1=...=4+2+1=...=4+3=3+4=5+1+1 
               =1+5+1=1+1+5=5+2=2+5=6+1=1+6 - Vladimir Baltic (baltic(AT)matf.bg.ac.yu), 
               Jan 17 2005
%D A001592 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001592 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001592 I. Flores, k-Generalized Fibonacci numbers, Fib. Quart., 5 (1967), 258-266.
%D A001592 Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas 
               n-step Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 
               05.4.4.
%H A001592 T. D. Noe, <a href="b001592.txt">Table of n, a(n) for n=0..200</a>
%H A001592 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Fxtbook</a>
%H A001592 P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               Sequences realized by oligomorphic permutation groups</a>, J. Integ. 
               Seqs. Vol. 3 (2000), #00.1.5.
%H A001592 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=13">
               Encyclopedia of Combinatorial Structures 13</a>
%H A001592 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A001592 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A001592 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Fibonaccin-StepNumber.html">Fibonacci n-Step Number</a>
%H A001592 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HexanacciNumber.html">Hexanacci Number</a>
%F A001592 x^5/(1 - x - x^2 - x^3 - x^4 - x^5 - x^6)
%p A001592 A001592:=-1/(-1+z+z**2+z**3+z**4+z**5+z**6); [S. Plouffe in his 1992 
               dissertation.]
%t A001592 CoefficientList[Series[x^5/(1 - x - x^2 - x^3 - x^4 - x^5 - x^6), {x, 
               0, 50}], x]
%Y A001592 Row 6 of arrays A048887 and A092921 (k-generalized Fibonacci numbers).
%Y A001592 Sequence in context: A145112 A062259 A001949 this_sequence A140134 A049886 
               A128901
%Y A001592 Adjacent sequences: A001589 A001590 A001591 this_sequence A001593 A001594 
               A001595
%K A001592 nonn,easy
%O A001592 0,8
%A A001592 N. J. A. Sloane (njas(AT)research.att.com).
%E A001592 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 16 2000

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