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

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

Author

Seiichi Manyama, Dec 01 2023

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A000621, A367794, A367637.

Cf. A005710, A101918.

Programs

PARI

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;

Formula

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