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A375289
Expansion of (1 - x + x^3)/((1 - x + x^3)^2 + 4*x^4).
1
1, 1, 1, 0, -5, -14, -26, -29, 5, 119, 348, 639, 708, -128, -2943, -8571, -15707, -17340, 3347, 72718, 211126, 386091, 424633, -87173, -1796760, -5200513, -9490312, -10398336, 2263553, 44394265, 128099033, 233273880, 254623403, -58615334, -1096863450, -3155300397
OFFSET
0,5
FORMULA
a(n) = 2*a(n-1) - a(n-2) - 2*a(n-3) - 2*a(n-4) - a(n-6).
a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n-4*k,2*k).
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec((1-x+x^3)/((1-x+x^3)^2+4*x^4))
(PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(2*n-4*k, 2*k));
CROSSREFS
Cf. A375279.
Sequence in context: A070722 A018829 A332623 * A070133 A246517 A306886
KEYWORD
sign
AUTHOR
Seiichi Manyama, Aug 10 2024
STATUS
approved