A371873 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+1,n-3*k).
1, 3, 10, 36, 135, 517, 2003, 7815, 30634, 120480, 475002, 1876294, 7422676, 29400192, 116567356, 462561572, 1836843591, 7298613997, 29016050831, 115408159467, 459209330821, 1827849895817, 7277945888781, 28986847296997, 115479393316211, 460159673245743
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, binomial(2*n+1, n-3*k));
Formula
a(n) = [x^n] 1/(((1-x)^3-x^3) * (1-x)^(n-1)).