A367637 -id:A367637 - cp's OEIS frontend

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

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).

A367800 G.f. A(x) satisfies A(x) = 1 / (1 - x * A(x^8)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 14, 18, 23, 29, 36, 44, 53, 64, 78, 96, 119, 148, 184, 228, 281, 345, 423, 519, 638, 786, 970, 1198, 1479, 1824, 2247, 2766, 3404, 4190, 5160, 6358, 7837, 9661, 11908, 14674, 18078, 22268, 27428, 33786, 41623

Offset: 0

Seiichi Manyama, Dec 01 2023

nonn

a(n) = A005710(n-1) up to n=72, but then the two sequences start to differ. - R. J. Mathar, Dec 04 2023

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A000621, A367794, A367637.

Cf. A005710, A101918.

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\8, v[j+1]*v[i-8*j])); v;

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/8)} a(k) * a(n-1-8*k).

cp's OEIS Frontend

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

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