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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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5
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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
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OFFSET
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0,2
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COMMENTS
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Traces of successive powers of pentanacci matrix. - Artur Jasinski, Jan 05 2007
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..199 from T. D. Noe)
Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
S. Saito, T. Tanaka, N. Wakabayashi, Combinatorial Remarks on the Cyclic Sum Formula for Multiple Zeta Values , J. Int. Seq. 14 (2011) # 11.2.4, Table 3.
Eric Weisstein's World of Mathematics, Lucas n-Step Number
Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1).
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FORMULA
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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. - Vladimir Kruchinin, Feb 22 2011
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MATHEMATICA
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LinearRecurrence[{1, 1, 1, 1, 1}, {1, 3, 7, 15, 31}, 60] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2012 *)
CoefficientList[Series[(1+2*x+3*x^2+4*x^3+5*x^4)/(1-x-x^2-x^3-x^4-x^5), {x, 0, 50}], x] (* G. C. Greubel, Jan 01 2018 *)
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PROG
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(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
(Magma) I:=[1, 3, 7, 15, 31]; [n le 5 select I[n] else Self(n-1) + Self(n-2) + Self(n-3) + Self(n-4) + Self(n-5): n in [1..30]]; // G. C. Greubel, Jan 01 2018
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CROSSREFS
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Essentially the same as A074048.
Sequence in context: A304078 A151338 A229006 * A276647 A006778 A007574
Adjacent sequences: A023421 A023422 A023423 * A023425 A023426 A023427
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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