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A023424
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Expansion of (1+2*x+3*x^2+4*x^3+5*x^4)/(1-x-x^2-x^3-x^4-x^5).
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4
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1, 3, 7, 15, 31, 57, 113, 223, 439, 863, 1695, 3333, 6553, 12883, 25327, 49791, 97887, 192441, 378329, 743775, 1462223, 2874655, 5651423, 11110405, 21842481, 42941187, 84420151, 165965647, 326279871, 641449337, 1261056193, 2479171199, 4873922247, 9581878847
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Traces of successive powers of pentanacci matrix. - Artur Jasinski (grafix(AT)csl.pl), Jan 05 2007
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LINKS
| T. D. Noe, Table of n, a(n) for n = 0..199
Eric Weisstein's World of Mathematics, Lucas n-Step Number
Index to sequences with linear recurrences with constant coefficients, signature (1,1,1,1,1)
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FORMULA
| a(n)=n*sum(k=1..n, 1/k*sum(r=0..k, binomial(k,r)*sum(m=0..r, binomial(r,m)*sum(j=0..m, binomial(m,j)*binomial(j,n-m-k-j-r))))), n>0.
[From Vladimir Kruchinin (kru(AT)ie.tusur.ru), Feb 22 2011]
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MATHEMATICA
| LinearRecurrence[{1, 1, 1, 1, 1}, {1, 3, 7, 15, 31}, 60] (* From Vladimir Joseph Stephan Orlovsky, Feb 08 2012 *)
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PROG
| (Maxima)
a(n):=n*sum(1/k*sum(binomial(k, r)*sum(binomial(r, m)*sum(binomial(m, j)*binomial(j, n-m-k-j-r), j, 0, m), m, 0, r), r, 0, k), k, 1, n);
(PARI) Vec((1+2*x+3*x^2+4*x^3+5*x^4)/(1-x-x^2-x^3-x^4-x^5)+O(x^100)) \\ Charles R Greathouse IV, Feb 24, 2011
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CROSSREFS
| Essentially the same as A074048.
Sequence in context: A043729 A137170 A151338 * A006778 A007574 A034480
Adjacent sequences: A023421 A023422 A023423 * A023425 A023426 A023427
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KEYWORD
| nonn,easy,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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