A037580 Base 8 digits are, in order, the first n terms of the periodic sequence with initial period 1,3.

1, 11, 89, 715, 5721, 45771, 366169, 2929355, 23434841, 187478731, 1499829849, 11998638795, 95989110361, 767912882891, 6143303063129, 49146424505035, 393171396040281, 3145371168322251, 25162969346578009, 201303754772624075, 1610430038180992601, 12883440305447940811

Offset

1,2

Links

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

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

Formula

From Colin Barker, Dec 27 2012: (Start)

a(n) = (11*8^n + 7*(-1)^n - 18)/63.

a(n) = 8*a(n-1) + a(n-2) - 8*a(n-3).

G.f.: x*(3*x+1)/((x-1)*(x+1)*(8*x-1)). (End)

E.g.f.: exp(-x)*(7 - 18*exp(2*x) + 11*exp(9*x))/63. - Elmo R. Oliveira, Dec 27 2025

Maple

a:= proc(n) a(n):= `if`(n=0, 0, 8*a(n-1)+2+(-1)^n) end:
seq(a(n), n=1..22);  # Alois P. Heinz, Dec 27 2025

Mathematica

CoefficientList[Series[(3 x + 1)/((x - 1) (x + 1) (8 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2013 *)
Table[FromDigits[PadRight[{}, n, {1, 3}], 8], {n, 30}] (* Harvey P. Dale, May 15 2019 *)

Prog

(Magma) [(11*8^n+7*(-1)^n-18)/63: n in [1..30]]; // Vincenzo Librandi, Oct 22 2013

Crossrefs

Cf. A007094, A037576, A037577, A037578, A037579, A037581, A037582.

Sequence in context: A201117 A081657 A226854 * A155607 A356323 A110252

Adjacent sequences: A037577 A037578 A037579 * A037581 A037582 A037583

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

More terms from Colin Barker, Dec 27 2012

Status

approved