A037517 Base 8 digits are, in order, the first n terms of the periodic sequence with initial period 2,0,1.

2, 16, 129, 1034, 8272, 66177, 529418, 4235344, 33882753, 271062026, 2168496208, 17347969665, 138783757322, 1110270058576, 8882160468609, 71057283748874, 568458269990992, 4547666159927937, 36381329279423498, 291050634235387984, 2328405073883103873, 18627240591064830986, 149017924728518647888

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (8,0,1,-8).

Formula

G.f.: x*(2+x^2) / ( (x-1)*(8*x-1)*(1+x+x^2) ). - R. J. Mathar, Nov 21 2011

a(1)=2, a(2)=16, a(3)=129, a(4)=1034, a(n)=8*a(n-1)+a(n-3)-8*a(n-4). - Harvey P. Dale, May 09 2015

a(n) = floor(129*8^n/511). - Christian Krause, Jun 05 2026

Mathematica

Module[{nn=20, d8}, d8=PadRight[{}, nn, {2, 0, 1}]; Table[FromDigits[Take[ d8, n], 8], {n, nn}]] (* or *) LinearRecurrence[{8, 0, 1, -8}, {2, 16, 129, 1034}, 20] (* Harvey P. Dale, May 09 2015 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -8, 1, 0, 8]^(n-1)*[2; 16; 129; 1034])[1, 1] \\ Charles R Greathouse IV, Jun 02 2026

Crossrefs

Sequence in context: A171451 A012459 A012463 * A037720 A022018 A067684

Adjacent sequences: A037514 A037515 A037516 * A037518 A037519 A037520

Keyword

nonn,base,easy,changed

Author

Clark Kimberling

Extensions

a(19)-a(23) from Christian Krause, Jun 5 2026

Status

approved