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

1,6

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).

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

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 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x*(1-2*x+x^4)/(1-2*x+x^6) )); // G. C. Greubel, Aug 25 2023
(SageMath)
def A124313_list(prec):
    P.<x> = 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

Crossrefs

Cf. A001591, A124312, A124314.

Sequence in context: A294123 A321048 A038085 * A049890 A351915 A262236

Adjacent sequences: A124310 A124311 A124312 * A124314 A124315 A124316

Keyword

nonn,easy

Author

Artur Jasinski, Oct 25 2006

Extensions

Edited by Ralf Stephan, Oct 20 2013

Status

approved