A355117 a(1) = 1; a(n+1) = Sum_{d|n} 4^(n/d - 1) * a(d).
1, 1, 5, 21, 89, 345, 1405, 5501, 22033, 87649, 350405, 1398981, 5596345, 22373561, 89492141, 357930301, 1431711857, 5726679153, 22906712645, 91626189381, 366504720137, 1466016390873, 5864065352173, 23456251396589, 93825005578001, 375299982311441, 1501199928316661
Offset: 1
Keywords
Programs
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Mathematica
a[1] = 1; a[n_] := a[n] = Sum[4^((n - 1)/d - 1) a[d], {d, Divisors[n - 1]}]; Table[a[n], {n, 1, 27}]
Formula
G.f.: x * ( 1 + Sum_{n>=1} a(n) * x^n / (1 - 4 * x^n) ).
a(n) ~ 4^(n-1) / 3.