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

0,6

Links

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

Formula

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

Prog

(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, v[j+1]*v[i-4*j])); v;
(Python)
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

Crossrefs

Cf. A000108, A000621, A367637, A367800.

Cf. A367653, A367692, A367694, A367720.

Sequence in context: A247084 A017898 A003269 * A352043 A087221 A352041

Adjacent sequences: A367791 A367792 A367793 * A367795 A367796 A367797

Keyword

nonn

Author

Seiichi Manyama, Nov 30 2023

Status

approved