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

Author

Paul Curtz, Jan 18 2009

Keywords

• nonn
• less

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).

Programs

Mathematica

CoefficientList[Series[(x^3 + x^2)/(3*x^2 - 4*x + 1), {x, 0, 50}], x] (* G. C. Greubel, Feb 21 2017 *)
LinearRecurrence[{4,-3},{0,0,1,5},30] (* Harvey P. Dale, May 19 2024 *)

PARI

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

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

Extensions

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