%I #11 May 07 2025 09:12:40

%S 1,6,27,104,366,1212,3842,11784,35223,103122,296805,842160,2360780,

%T 6549240,18004980,49106992,132996957,357948894,957993823,2550977112,

%U 6761742234,17848312884,46932923478,122980461816

%N Pell numbers A000129(n+1) (without P(0)) convoluted twice with itself.

%C a(n)= A054456(n+2,2) (third column of Pell convolution triangle).

%H Milan Janjić, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Janjic/janjic33.html">Hessenberg Matrices and Integer Sequences</a>, J. Int. Seq. 13 (2010) # 10.7.8, section 3.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,-4,9,6,1)

%F a(n) = ((10*n^2+39*n+32)*P(n+1)+(n+1)*(4*n+11)*P(n))/32, where P(n)=A000129(n).

%F G.f.: 1/(1-2*x-x^2)^3.

%F a(n) = F''(n+3, 2)/2, that is, 1/2 times the 2nd derivative of the (n+3)th Fibonacci polynomial evaluated at x=2. - _T. D. Noe_, Jan 19 2006

%Y Cf. A054456, A000129, A006645.

%K easy,nonn

%O 0,2

%A _Wolfdieter Lang_, Apr 27 2000