A360901 G.f. satisfies A(x) = 1 + x/(1 + x^4)^2 * A(x/(1 + x^4)).
1, 1, 1, 1, 1, -1, -4, -8, -13, -16, -3, 39, 126, 273, 411, 283, -619, -3149, -8201, -14496, -14368, 12984, 109920, 329552, 655436, 785583, -312525, -5009034, -16789151, -36433571, -48990090, 6965306, 286109557, 1044072824, 2414264953, 3490255449, -41486331
Offset: 0
Keywords
Programs
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PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\4, (-1)^j*binomial(i-3*j, j)*v[i-4*j])); v;
Formula
a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} (-1)^k * binomial(n-3*k,k) * a(n-1-4*k).