OFFSET
0,2
COMMENTS
Traces of successive powers of pentanacci matrix. - Artur Jasinski, Jan 05 2007
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..199 from T. D. Noe)
Shingo Saito, Tatsushi Tanaka, and Noriko Wakabayashi, Combinatorial Remarks on the Cyclic Sum Formula for Multiple Zeta Values, J. Int. Seq. 14 (2011) # 11.2.4, Table 3.
Igor Szczyrba, Rafał Szczyrba, and Martin Burtscher, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
Eric Weisstein's World of Mathematics, Lucas n-Step Number
Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1).
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. - Vladimir Kruchinin, Feb 22 2011
MATHEMATICA
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 *)
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
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved