A098577 a(n) = Sum_{k=0..floor(n/5)} C(n-3*k,2*k) * 2^k.

1, 1, 1, 1, 1, 3, 7, 13, 21, 31, 47, 77, 133, 231, 391, 645, 1053, 1727, 2863, 4781, 7989, 13303, 22071, 36565, 60621, 100655, 167295, 278077, 461989, 767143, 1273607, 2114661, 3511869, 5833055, 9688527, 16091213, 26723221, 44378967, 73700823

Offset

0,6

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,2).

Formula

G.f.: (1-x)/((1-x)^2-2*x^5).

a(n) = a(n-1) - a(n-2) + 2*a(n-5).

a(n) = hypergeom([(1-n)/5, (2-n)/5, (3-n)/5, (4-n)/5, -n/5], [1/2, (1-n)/3, (2-n)/3, -n/3], 5^5/(2*3^3)). - Stefano Spezia, Sep 09 2025

Mathematica

LinearRecurrence[{2, -1, 0, 0, 2}, {1, 1, 1, 1, 1}, 40] (* Harvey P. Dale, Feb 11 2015 *)
CoefficientList[Series[(1-x)/((1-x)^2-2*x^5), {x, 0, 50}], x] (* G. C. Greubel, Feb 03 2018 *)

Prog

(PARI) my(x='x+O('x^30)); Vec((1-x)/((1-x)^2-2*x^5)) \\ G. C. Greubel, Feb 03 2018
(Magma) I:=[1, 1, 1, 1, 1, ]; [n le 5 select I[n] else 2*Self(n-1) -Self(n-2) + 2*Self(n-5): n in [1..30]]; // G. C. Greubel, Feb 03 2018

Crossrefs

Cf. A098575, A005253.

Sequence in context: A206246 A171965 A011898 * A004136 A387599 A335865

Adjacent sequences: A098574 A098575 A098576 * A098578 A098579 A098580

Keyword

easy,nonn

Author

Paul Barry, Sep 16 2004

Status

approved