A033136 Base 9 digits are, in order, the first n terms of the periodic sequence with initial period 1,1,0.

1, 10, 90, 811, 7300, 65700, 591301, 5321710, 47895390, 431058511, 3879526600, 34915739400, 314241654601, 2828174891410, 25453574022690, 229082166204211, 2061739495837900, 18555655462541100, 167000899162869901, 1503008092465829110, 13527072832192461990

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Index entries for linear recurrences with constant coefficients, signature (9,0,1,-9).

Formula

G.f.: x*(1+x) / ( (x-1)*(9*x-1)*(1+x+x^2) ). a(n) = A033145(n) + A033145(n-1). - R. J. Mathar, Jan 08 2011

a(n) = round( (45/364)*9^n ). - Tani Akinari, Jul 15 2014

a(n+1) = 9*a(n) if n == 2 (mod 3), 9*a(n)+1 otherwise. - Robert Israel, Jul 15 2014

Example

The first six terms have base 9 representations 1, 11, 110, 1101, 11011, 110110.

Mathematica

Module[{nn=30, c}, c=PadRight[{}, nn, {1, 1, 0}]; Table[FromDigits[Take[c, n], 9], {n, nn}]] (* Harvey P. Dale, Aug 18 2014 *)

Prog

(PARI) Vec(x*(1+x) / ( (x-1)*(9*x-1)*(1+x+x^2) ) + O(x^50)) \\ Michel Marcus, Jul 15 2014

Crossrefs

Cf. A033137 (similar in base 10).

Sequence in context: A170691 A003952 A252703 * A061206 A199527 A137684

Adjacent sequences: A033133 A033134 A033135 * A033137 A033138 A033139

Keyword

nonn,base,easy

Author

Clark Kimberling

Extensions

More terms from Michel Marcus, Jul 15 2014

Status

approved