A117439 Expansion of (1-x^2)/(1 -4*x -2*x^2 +x^4).

1, 4, 17, 76, 337, 1496, 6641, 29480, 130865, 580924, 2578785, 11447508, 50816737, 225581040, 1001378849, 4445229968, 19732860833, 87596322228, 388849631729, 1726145941404, 7662550168241, 34014896233544, 150995835638929, 670286989081400, 2975477077435217, 13208467391670124, 58633827885912001, 260281959337906852

Offset

0,2

Comments

Row sums of unsigned version of number triangle A117438.

Links

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

Index entries for linear recurrences with constant coefficients, signature (4,2,0,-1).

Formula

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

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

Mathematica

LinearRecurrence[{4, 2, 0, -1}, {1, 4, 17, 76}, 40] (* G. C. Greubel, Jun 01 2021 *)

Prog

(Magma) I:=[1, 4, 17, 76]; [n le 4 select I[n] else 4*Self(n-1) +2*Self(n-2) -Self(n-4): n in [1..41]]; // G. C. Greubel, Jun 01 2021
(Sage)
def A117439_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1-x^2)/(1-4*x-2*x^2+x^4) ).list()
A117439_list(40) # G. C. Greubel, Jun 01 2021

Crossrefs

Cf. A117438.

Sequence in context: A255714 A151247 A290914 * A081910 A026773 A081186

Adjacent sequences: A117436 A117437 A117438 * A117440 A117441 A117442

Keyword

easy,nonn

Author

Paul Barry, Mar 16 2006

Extensions

Terms a(23) onward added by G. C. Greubel, Jun 01 2021

Status

approved