A355116 - OEIS

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

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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.