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A376716
Expansion of (1 - x + x^2)/((1 - x + x^2)^2 - 4*x^2).
4
1, 1, 4, 11, 27, 72, 189, 493, 1292, 3383, 8855, 23184, 60697, 158905, 416020, 1089155, 2851443, 7465176, 19544085, 51167077, 133957148, 350704367, 918155951, 2403763488, 6293134513, 16475640049, 43133785636, 112925716859, 295643364939, 774004377960
OFFSET
0,3
FORMULA
a(n) = 2*a(n-1) + a(n-2) + 2*a(n-3) - a(n-4).
a(n) = Sum_{k=0..floor(n/2)} binomial(2*n-2*k+1,2*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec((1-x+x^2)/((1-x+x^2)^2-4*x^2))
(PARI) a(n) = sum(k=0, n\2, binomial(2*n-2*k+1, 2*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 02 2024
STATUS
approved