A154992 - OEIS

%I #11 May 19 2024 14:45:00

%S 0,0,1,5,17,53,161,485,1457,4373,13121,39365,118097,354293,1062881,

%T 3188645,9565937,28697813,86093441,258280325,774840977,2324522933,

%U 6973568801,20920706405,62762119217,188286357653,564859072961

%N A048473 prefixed by two zeros.

%C 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).

%H G. C. Greubel, <a href="/A154992/b154992.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4, -3).

%F a(n) = A048473(n-2) = 3*2^(n-2)-1, n>1. - _R. J. Mathar_, Jan 23 2009

%F G.f.: (x^3 + x^2)/(3*x^2 - 4*x + 1). - _Alexander R. Povolotsky_, Feb 21 2009

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

%t LinearRecurrence[{4,-3},{0,0,1,5},30] (* _Harvey P. Dale_, May 19 2024 *)

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

%K nonn,less

%O 0,4

%A _Paul Curtz_, Jan 18 2009

%E Edited and extended by _R. J. Mathar_, Jan 23 2009