A360891 -id:A360891 - cp's OEIS frontend

A360890 G.f. satisfies A(x) = 1 + x/(1 - x^3) * A(x/(1 - x^3)).

1, 1, 1, 1, 2, 4, 7, 12, 25, 55, 115, 245, 564, 1331, 3103, 7407, 18388, 46198, 116503, 299966, 789426, 2095941, 5616114, 15299205, 42255533, 117689096, 331204936, 944052610, 2718150015, 7891518587, 23137661717, 68524545717, 204645635263, 616098009473

Offset: 0

Seiichi Manyama, Feb 25 2023

nonn

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

Cf. A000110, A172383, A360891.

Cf. A360898.

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

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

A360899 G.f. satisfies A(x) = 1 + x/(1 + x^4) * A(x/(1 + x^4)).

Original entry on oeis.org

1, 1, 1, 1, 1, 0, -2, -5, -9, -13, -10, 10, 60, 155, 281, 325, 5, -1214, -4094, -8786, -12571, -5642, 35339, 149264, 363838, 596714, 417156, -1373639, -7048541, -18932245, -34095357, -29271979, 68706873, 413250742, 1193425228, 2293494882, 2201716631

Offset: 0

Seiichi Manyama, Feb 25 2023

sign

Cf. A172385, A360898.

Cf. A360891.

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-1-3*j, j)*v[i-4*j])); v;

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

A360890 G.f. satisfies A(x) = 1 + x/(1 - x^3) * A(x/(1 - x^3)).

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A360899 G.f. satisfies A(x) = 1 + x/(1 + x^4) * A(x/(1 + x^4)).

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Crossrefs

Programs

PARI

Formula

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

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Author

Keywords

Crossrefs

Programs

PARI

Formula