A154992 A048473 prefixed by two zeros.

0, 0, 1, 5, 17, 53, 161, 485, 1457, 4373, 13121, 39365, 118097, 354293, 1062881, 3188645, 9565937, 28697813, 86093441, 258280325, 774840977, 2324522933, 6973568801, 20920706405, 62762119217, 188286357653, 564859072961

Offset

0,4

Comments

Consider two generic sequences correlated via c(n)=b(n) mod p. The difference d(n)=b(n)-c(n) contains only multiples of p and a(n)=d(n)/p defines another integer sequence. This sequence here takes b(n)=A048473(n) with p=9, such that c(n)=1,5,8,8,8,.. (period 8 continued). Then d(n)= 0,0,9,45,153,477,1449,.. becomes 9 times (two zeros followed by A048473) and division through 9 generates a(n) as the shifted version of b(n)=A048374(n).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4, -3).

Formula

a(n) = A048473(n-2) = 3*2^(n-2)-1, n>1. - R. J. Mathar, Jan 23 2009

G.f.: (x^3 + x^2)/(3*x^2 - 4*x + 1). - Alexander R. Povolotsky, Feb 21 2009

Mathematica

CoefficientList[Series[(x^3 + x^2)/(3*x^2 - 4*x + 1), {x, 0, 50}], x] (* G. C. Greubel, Feb 21 2017 *)

Prog

(PARI) x='x+O('x^50); Vec((x^3 + x^2)/(3*x^2 - 4*x + 1)) \\ G. C. Greubel, Feb 21 2017

Crossrefs

Sequence in context: A027028 A176086 A048473 * A178828 A242429 A097160

Adjacent sequences: A154989 A154990 A154991 * A154993 A154994 A154995

Keyword

nonn,less

Author

Paul Curtz, Jan 18 2009

Extensions

Edited and extended by R. J. Mathar, Jan 23 2009

Status

approved