%I #9 Dec 07 2022 12:36:59
%S 1,12,108,848,6192,43200,292224,1933056,12572928,80702464,512532480,
%T 3226742784,20166803456,125262102528,773910872064,4759428268032,
%U 29151365234688,177913041518592,1082361265782784,6565932190138368
%N Convolution of A111989 with itself.
%H Harvey P. Dale, <a href="/A111990/b111990.txt">Table of n, a(n) for n = 0..1000</a>
%H W. Lang, <a href="http://www.fq.math.ca/Papers1/42-3/quartlang03_2004.pdf">Riccati meets Fibonacci</a>, The Fibonacci Quarterly, 42 (2004) pp. 231-244, eqs.(58),(59).
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (12, -36, -16, 96, 0, -64).
%F G.f.: 1/(1-6*x+8*x^3)^2.
%F a(n) = (2*(n+1)*b(n+1)-(n+3)*b(n)-4*(n+2)*b(n-1))/9, with b(n):=A111989(n).
%t 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 *)
%o (PARI) Vec(1/(1-6*x+8*x^3)^2 + O(x^30)) \\ _Michel Marcus_, Mar 11 2016
%Y Cf. A111991 (second convolution of A111989).
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Sep 12 2005