A355116 a(1) = 1; a(n+1) = Sum_{d|n} 3^(n/d - 1) * a(d).

1, 1, 4, 13, 43, 124, 388, 1117, 3370, 9967, 29860, 88909, 266896, 798337, 2394553, 7178233, 21533029, 64579750, 193738672, 581159161, 1743472426, 5230263235, 15690765067, 47071824676, 141215472685, 423645012649, 1270934954221, 3812800839124, 11438402333398, 34315194788359

Offset

1,3

Links

Table of n, a(n) for n=1..30.

Formula

G.f.: x * ( 1 + Sum_{n>=1} a(n) * x^n / (1 - 3 * x^n) ).

a(n) ~ 3^(n-1) / 2.

Mathematica

a[1] = 1; a[n_] := a[n] = Sum[3^((n - 1)/d - 1) a[d], {d, Divisors[n - 1]}]; Table[a[n], {n, 1, 30}]

Crossrefs

Cf. A003238, A351405, A355117.

Sequence in context: A149425 A047144 A072307 * A266494 A121486 A339063

Adjacent sequences: A355113 A355114 A355115 * A355117 A355118 A355119

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 19 2022

Status

approved