The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A355117

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A355117

a(1) = 1; a(n+1) = Sum_{d|n} 4^(n/d - 1) * a(d).
(history; published version)

#5 by Michael De Vlieger at Fri Jun 24 08:30:39 EDT 2022

STATUS

reviewed

approved

#4 by Joerg Arndt at Fri Jun 24 05:00:47 EDT 2022

STATUS

proposed

reviewed

#3 by Ilya Gutkovskiy at Sun Jun 19 13:30:39 EDT 2022

STATUS

editing

proposed

#2 by Ilya Gutkovskiy at Sun Jun 19 13:21:02 EDT 2022

NAME

allocated for Ilya Gutkovskiy

a(1) = 1; a(n+1) = Sum_{d|n} 4^(n/d - 1) * a(d).

DATA

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

1,3

FORMULA

G.f.: x * ( 1 + Sum_{n>=1} a(n) * x^n / (1 - 4 * x^n) ).

a(n) ~ 4^(n-1) / 3.

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}]

CROSSREFS

Cf. A003238, A351405, A355116.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Jun 19 2022

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Sun Jun 19 13:21:02 EDT 2022

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved