A037569 Base 4 digits are, in order, the first n terms of the periodic sequence with initial period 2,1,2.

2, 9, 38, 154, 617, 2470, 9882, 39529, 158118, 632474, 2529897, 10119590, 40478362, 161913449, 647653798, 2590615194, 10362460777, 41449843110, 165799372442, 663197489769, 2652789959078, 10611159836314, 42444639345257, 169778557381030, 679114229524122, 2716456918096489, 10865827672385958

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: x*(2+x+2*x^2) / ((x-1)*(4*x-1)*(1+x+x^2)). - R. J. Mathar, Nov 21 2011

a(n) = 4*(n-1) + a(n-3) - 4*a(n-4). - Vincenzo Librandi, Jun 17 2012

a(n) = floor(38*4^n/63). - Christian Krause, Jun 05 2026

Mathematica

With[{c=PadRight[{}, 30, {2, 1, 2}]}, Table[FromDigits[Take[c, n], 4], {n, 30}]] (* Harvey P. Dale, Nov 06 2011 *)
LinearRecurrence[{4, 0, 1, -4}, {2, 9, 38, 154}, 40] (* Vincenzo Librandi, Jun 17 2012 *)

Prog

(Magma) I:=[2, 9, 38, 154]; [n le 4 select I[n] else 4*Self(n-1)+Self(n-3)-4*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jun 17 2012
(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -4, 1, 0, 4]^(n-1)*[2; 9; 38; 154])[1, 1] \\ Charles R Greathouse IV, Jun 02 2026

Crossrefs

Sequence in context: A181339 A291265 A037489 * A291462 A001077 A150993

Adjacent sequences: A037566 A037567 A037568 * A037570 A037571 A037572

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

a(24)-a(27) from Christian Krause, Jun 05 2026

Status

approved