A098576 a(n) = Sum_{k=0..floor(n/4)} C(n-2*k,2*k) * 3^k.

1, 1, 1, 1, 4, 10, 19, 31, 55, 109, 220, 424, 793, 1489, 2845, 5473, 10480, 19954, 37963, 72391, 138259, 263989, 503608, 960400, 1831969, 3495505, 6669865, 12725425, 24276892, 46314874, 88362451, 168586303, 321640831, 613639981, 1170726484

Offset

0,5

Links

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

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,3).

Formula

G.f.: (1-x)/((1-x)^2-3*x^4).

a(n) = 2*a(n-1) - a(n-2) + 3*a(n-4).

Mathematica

Table[Sum[Binomial[n-2k, 2k]3^k, {k, 0, Floor[n/4]}], {n, 0, 40}] (* or *) LinearRecurrence[{2, -1, 0, 3}, {1, 1, 1, 1}, 40] (* Harvey P. Dale, Dec 04 2011 *)

Prog

(PARI) x='x+O('x^30); Vec((1-x)/((1-x)^2-3*x^4)) \\ G. C. Greubel, Feb 03 2018
(Magma) I:=[1, 1, 1, 1]; [n le 4 select I[n] else 2*Self(n-1) - Self(n-2) + 3*Self(n-4): n in [1..30]]; // G. C. Greubel, Feb 03 2018

Crossrefs

Cf. A097116, A098575.

Sequence in context: A027371 A301022 A301119 * A063773 A155432 A155302

Adjacent sequences: A098573 A098574 A098575 * A098577 A098578 A098579

Keyword

easy,nonn

Author

Paul Barry, Sep 16 2004

Status

approved