A054457 Pell numbers A000129(n+1) (without P(0)) convoluted twice with itself.

1, 6, 27, 104, 366, 1212, 3842, 11784, 35223, 103122, 296805, 842160, 2360780, 6549240, 18004980, 49106992, 132996957, 357948894, 957993823, 2550977112, 6761742234, 17848312884, 46932923478, 122980461816

Offset: 0

Author

Wolfdieter Lang, Apr 27 2000

Keywords

• easy
• nonn

Comments

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

Links

• Milan Janjić, Hessenberg Matrices and Integer Sequences, J. Int. Seq. 13 (2010) # 10.7.8, section 3.
• Index entries for linear recurrences with constant coefficients, signature (6,-9,-4,9,6,1)

Crossrefs

Cf. A054456, A000129, A006645.

Formula

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

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

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