A367800 -id:A367800 - cp's OEIS frontend

A367637 G.f. A(x) satisfies A(x) = 1 / (1 - x * A(x^6)).

1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 9, 12, 16, 21, 27, 34, 43, 55, 71, 92, 119, 153, 196, 251, 322, 414, 533, 686, 882, 1133, 1455, 1869, 2402, 3088, 3970, 5103, 6558, 8427, 10829, 13917, 17888, 22992, 29551, 37979, 48809, 62727, 80617, 103612, 133167

Offset: 0

Seiichi Manyama, Dec 01 2023

nonn

This sequence is different from A005708.

Seiichi Manyama, Table of n, a(n) for n = 0..5000

Cf. A000621, A367794, A367800.

Cf. A005708, A101916.

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\6, v[j+1]*v[i-6*j])); v;

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/6)} a(k) * a(n-1-6*k).

A367794 G.f. A(x) satisfies A(x) = 1 / (1 - x * A(x^4)).

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 3, 4, 5, 7, 10, 14, 19, 26, 36, 50, 69, 95, 131, 181, 250, 346, 478, 660, 911, 1259, 1740, 2404, 3320, 4586, 6336, 8754, 12093, 16705, 23077, 31881, 44043, 60844, 84053, 116116, 160410, 221602, 306136, 422916, 584242, 807110, 1114996

Offset: 0

Seiichi Manyama, Nov 30 2023

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..5000

Cf. A000108, A000621, A367637, A367800.

Cf. A367653, A367692, A367694, A367720.

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

from functools import lru_cache
@lru_cache(maxsize=None)
def A367794(n): return sum(A367794(k)*A367794(n-1-(k<<2)) for k in range(n+3>>2)) if n else 1 # Chai Wah Wu, Nov 30 2023

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

cp's OEIS Frontend

A367637 G.f. A(x) satisfies A(x) = 1 / (1 - x * A(x^6)).

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