A357238 Inverse Moebius transform of tribonacci numbers (A000073).

0, 1, 1, 3, 4, 9, 13, 27, 45, 86, 149, 285, 504, 941, 1710, 3163, 5768, 10662, 19513, 35978, 66026, 121565, 223317, 411053, 755480, 1390042, 2555802, 4701713, 8646064, 15904390, 29249425, 53801243, 98950246, 182003370, 334745794, 615704412, 1132436852, 2082895617, 3831006934

Offset

1,4

Links

Table of n, a(n) for n=1..39.

Formula

G.f.: Sum_{k>=1} x^(2*k) / (1 - x^k - x^(2*k) - x^(3*k)).

G.f.: Sum_{k>=1} A000073(k) * x^k / (1 - x^k).

a(n) = Sum_{d|n} A000073(d).

Mathematica

nmax = 39; CoefficientList[Series[Sum[x^(2 k)/(1 - x^k - x^(2 k) - x^(3 k)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Prog

(PARI) f(n) = ([0, 1, 0; 0, 0, 1; 1, 1, 1]^n)[1, 3]; \\ A000073
a(n) = sumdiv(n, d, f(d)); \\ Michel Marcus, Sep 20 2022

Crossrefs

Cf. A000073, A007435, A357239.

Sequence in context: A000624 A244703 A232801 * A056514 A151517 A219043

Adjacent sequences: A357235 A357236 A357237 * A357239 A357240 A357241

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 19 2022

Status

approved