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 *)
LinearRecurrence[{4, -3}, {0, 0, 1, 5}, 30] (* Harvey P. Dale, May 19 2024 *)
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
KEYWORD
nonn,less
AUTHOR
Paul Curtz, Jan 18 2009
EXTENSIONS
Edited and extended by R. J. Mathar, Jan 23 2009
STATUS
approved