A037611 Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,3,2.

1, 7, 30, 121, 487, 1950, 7801, 31207, 124830, 499321, 1997287, 7989150, 31956601, 127826407, 511305630, 2045222521, 8180890087, 32723560350, 130894241401, 523576965607, 2094307862430, 8377231449721, 33508925798887, 134035703195550, 536142812782201, 2144571251128807

Offset

1,2

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

Index entries for 2-automatic sequences.

Index entries for linear recurrences with constant coefficients, signature (4,0,1,-4).

Formula

From R. J. Mathar, Apr 27 2015: (Start)

G.f.: x*(1+x)*(2*x+1) / ( (x-1)*(4*x-1)*(1+x+x^2) ).

A007090(a(n)) = A037617(n). (End)

a(n) ~ (10/21)*4^n = (10/21)*A000302(n). - Stefano Spezia, Oct 15 2023

Mathematica

LinearRecurrence[{4, 0, 1, -4}, {1, 7, 30, 121}, 30] (* Paolo Xausa, Oct 16 2023 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -4, 1, 0, 4]^(n-1)*[1; 7; 30; 121])[1, 1] \\ Charles R Greathouse IV, Feb 13 2017

Crossrefs

Cf. A000302, A007090, A037617.

Sequence in context: A026631 A037709 A378502 * A171472 A369201 A220720

Adjacent sequences: A037608 A037609 A037610 * A037612 A037613 A037614

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

a(24)-a(26) from Stefano Spezia, Oct 15 2023

Status

approved