A124313 Pentanacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5), starting 1,0,0,0,1.

1, 0, 0, 0, 1, 2, 3, 6, 12, 24, 47, 92, 181, 356, 700, 1376, 2705, 5318, 10455, 20554, 40408, 79440, 156175, 307032, 603609, 1186664, 2332920, 4586400, 9016625, 17726218, 34848827, 68510990, 134689060, 264791720, 520566815, 1023407412

Offset: 1

Author

Artur Jasinski, Oct 25 2006

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• I. Flores, k-Generalized Fibonacci numbers, Fib. Quart., 5 (1967), 258-266.
• Eric Weisstein's World of Mathematics, Pentanacci Number
• Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1).

Crossrefs

Cf. A001591, A124312, A124314.

Programs

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x*(1-2*x+x^4)/(1-2*x+x^6) )); // G. C. Greubel, Aug 25 2023

Mathematica

f[n_]:= MatrixPower[{{1,1,1,1,1}, {1,0,0,0,0}, {0,1,0,0,0}, {0,0,1,0, 0}, {0,0,0,1,0}}, n][[ 1, 4]]; Array[f, 50]
LinearRecurrence[{1,1,1,1,1}, {1,0,0,0,1}, 40] (* G. C. Greubel, Aug 25 2023 *)

SageMath

def A124313_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1-2*x+x^4)/(1-2*x+x^6) ).list()
A124313_list(50) # G. C. Greubel, Aug 25 2023

Formula

G.f.: x*(1-x-x^2-x^3)/(1-x-x^2-x^3-x^4-x^5). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009; checked and corrected by R. J. Mathar, Sep 16 2009

Extensions

Edited by Ralf Stephan, Oct 20 2013