A111990 Convolution of A111989 with itself.
1, 12, 108, 848, 6192, 43200, 292224, 1933056, 12572928, 80702464, 512532480, 3226742784, 20166803456, 125262102528, 773910872064, 4759428268032, 29151365234688, 177913041518592, 1082361265782784, 6565932190138368
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000
- W. Lang, Riccati meets Fibonacci, The Fibonacci Quarterly, 42 (2004) pp. 231-244, eqs.(58),(59).
- Index entries for linear recurrences with constant coefficients, signature (12, -36, -16, 96, 0, -64).
Programs
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Mathematica
CoefficientList[Series[1/(1-6x+8x^3)^2,{x,0,30}],x] (* or *) LinearRecurrence[{12,-36,-16,96,0,-64},{1,12,108,848,6192,43200},30] (* Harvey P. Dale, Dec 07 2022 *) -
PARI
Vec(1/(1-6*x+8*x^3)^2 + O(x^30)) \\ Michel Marcus, Mar 11 2016
Formula
G.f.: 1/(1-6*x+8*x^3)^2.
a(n) = (2*(n+1)*b(n+1)-(n+3)*b(n)-4*(n+2)*b(n-1))/9, with b(n):=A111989(n).