A157459 Expansion of 72*x^2 / (1 - 323*x + 323*x^2 - x^3).
0, 72, 23256, 7488432, 2411251920, 776415629880, 250003421569512, 80500325329753056, 25920854752758914592, 8346434730063040745640, 2687526062225546361181560, 865375045601895865259716752, 278648077157748243067267612656, 89723815469749332371794911558552
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..250
- Index entries for linear recurrences with constant coefficients, signature (323,-323,1).
Programs
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Mathematica
LinearRecurrence[{323,-323,1},{0,72,23256},20] (* Harvey P. Dale, Feb 28 2021 *) -
PARI
concat(0, Vec(72*x^2/(1-323*x+323*x^2-x^3)+O(x^20))) \\ Charles R Greathouse IV, Sep 26 2012
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PARI
a(n) = -round((161+72*sqrt(5))^(-n)*(-1+(161+72*sqrt(5))^n)*(9+4*sqrt(5)+(-9+4*sqrt(5))*(161+72*sqrt(5))^n))/80 \\ Colin Barker, Jul 25 2016
Formula
4*a(n) + 1 = A007805(n-1)^2.
5*a(n) + 1 = A049629(n-1)^2.
G.f.: 72*x^2/(1 - 323*x + 323*x^2 - x^3).
c(1) = 0, c(2) = 72, c(3) = 323*c(2), c(n) = 323*(c(n-1) - c(n-2)) + c(n-3) for n>3.
a(n) = -((161+72*sqrt(5))^(-n)*(-1+(161+72*sqrt(5))^n)*(9+4*sqrt(5)+(-9+4*sqrt(5))*(161+72*sqrt(5))^n))/80. - Colin Barker, Jul 25 2016
a(n) = 72*A298271(n-1). - Greg Dresden, Dec 02 2021
a(n) = 2*A201003(n-1). - Amiram Eldar, Dec 01 2024
Extensions
Edited by Alois P. Heinz, Sep 09 2011
Comments