A037709 Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,3,2,0.

1, 7, 30, 120, 481, 1927, 7710, 30840, 123361, 493447, 1973790, 7895160, 31580641, 126322567, 505290270, 2021161080, 8084644321, 32338577287, 129354309150, 517417236600, 2069668946401, 8278675785607, 33114703142430, 132458812569720, 529835250278881, 2119341001115527, 8477364004462110, 33909456017848440, 135637824071393761, 542551296285575047

Offset

1,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (5,-5,5,-4).

Formula

G.f.: x*(1+2*x) / ( (x-1)*(4*x-1)*(x^2+1) ). - R. J. Mathar, Oct 13 2015

a(n) ~ (8/17)*4^n = (8/17)*A000302(n). - Stefano Spezia, Oct 16 2023

Mathematica

LinearRecurrence[{5, -5, 5, -4}, {1, 7, 30, 120}, 30] (* Stefano Spezia, Oct 16 2023 *)
Table[FromDigits[PadRight[{}, n, {1, 3, 2, 0}], 4], {n, 30}] (* Harvey P. Dale, Apr 07 2026 *)

Crossrefs

Sequence in context: A269084 A055269 A026631 * A378502 A037611 A171472

Adjacent sequences: A037706 A037707 A037708 * A037710 A037711 A037712

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

a(24)-a(26) from Stefano Spezia, Oct 16 2023

Corrected and extended by Harvey P. Dale, Apr 07 2026

Status

approved