A360892 -id:A360892 - cp's OEIS frontend

A360900 G.f. satisfies A(x) = 1 + x/(1 + x^3)^2 * A(x/(1 + x^3)).

1, 1, 1, 1, -1, -4, -8, -10, 2, 40, 115, 174, 22, -736, -2495, -4276, -920, 20593, 75011, 135814, 17524, -788871, -2909061, -5248648, 623274, 38581252, 138036877, 235567666, -134440249, -2284840691, -7698637124, -11745925435, 15869626983, 157479613343

Offset: 0

Seiichi Manyama, Feb 25 2023

sign

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Cf. A352865, A360901.

Cf. A360892.

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\3, (-1)^j*binomial(i-2*j, j)*v[i-3*j])); v;

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} (-1)^k * binomial(n-2*k,k) * a(n-1-3*k).

A360893 G.f. satisfies A(x) = 1 + x/(1 - x^4)^2 * A(x/(1 - x^4)).

Original entry on oeis.org

1, 1, 1, 1, 1, 3, 6, 10, 15, 24, 51, 109, 214, 389, 747, 1595, 3497, 7379, 15065, 31750, 70504, 159352, 353748, 777240, 1742696, 4022595, 9379659, 21717264, 50239529, 117913537, 281584044, 676667552, 1623733085, 3908144320, 9509212539, 23393422297, 57815808829

Offset: 0

Seiichi Manyama, Feb 25 2023

nonn

Cf. A040027, A352864, A360892.

Cf. A360891, A360901.

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\4, binomial(i-3*j, j)*v[i-4*j])); v;

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n-3*k,k) * a(n-1-4*k).

cp's OEIS Frontend

A360900 G.f. satisfies A(x) = 1 + x/(1 + x^3)^2 * A(x/(1 + x^3)).

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