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A307395 Expansion of 1/((1 - x) * ((1 - x)^3 + x^3)). 2
1, 4, 10, 19, 28, 28, 1, -80, -242, -485, -728, -728, 1, 2188, 6562, 13123, 19684, 19684, 1, -59048, -177146, -354293, -531440, -531440, 1, 1594324, 4782970, 9565939, 14348908, 14348908, 1, -43046720, -129140162, -258280325, -387420488, -387420488, 1, 1162261468 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..4000

Index entries for linear recurrences with constant coefficients, signature (4,-6,3).

FORMULA

a(n) = Sum_{k=0..floor(n/3)} (-1)^k*binomial(n+3,3*k+3).

a(n) = 4*a(n-1) - 6*a(n-2) + 3*a(n-3) for n > 2.

a(6*n) = 1.

PROG

(PARI) {a(n) = sum(k=0, n\3, (-1)^k*binomial(n+3, 3*k+3))}

(PARI) N=66; x='x+O('x^N); Vec(1/((1-x)*((1-x)^3+x^3)))

CROSSREFS

Column 5 of A307394.

Partial sums of A057083.

Sequence in context: A073262 A145731 A162958 * A029714 A062198 A050858

Adjacent sequences:  A307392 A307393 A307394 * A307396 A307397 A307398

KEYWORD

sign,easy

AUTHOR

Seiichi Manyama, Apr 07 2019

STATUS

approved

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Last modified April 22 10:58 EDT 2021. Contains 343174 sequences. (Running on oeis4.)