A367717 G.f. A(x) satisfies A(x) = 1 / ((1 + x) * (1 - x * (1 + x + x^2) * A(x^3))).

1, 0, 2, 2, 5, 8, 16, 30, 57, 108, 206, 390, 741, 1407, 2670, 5068, 9622, 18262, 34666, 65806, 124911, 237109, 450092, 854368, 1621784, 3078519, 5843709, 11092672, 21056400, 39969753, 75871567, 144021302, 273384733, 518945611, 985075356, 1869894158, 3549478993

Offset

0,3

Links

Table of n, a(n) for n=0..36.

Formula

a(n) = (-1)^n + Sum_{k=0..n-1} a(floor(k/3)) * a(n-1-k).

Prog

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

Crossrefs

Cf. A005043, A367716, A367718.

Cf. A367693, A367714.

Sequence in context: A246807 A077902 A005834 * A052531 A257517 A337079

Adjacent sequences: A367714 A367715 A367716 * A367718 A367719 A367720

Keyword

nonn

Author

Seiichi Manyama, Nov 28 2023

Status

approved