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

0,2

Comments

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

Links

Table of n, a(n) for n=0..23.

M. Janjic, 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)

Formula

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

Crossrefs

Cf. A054456, A000129, A006645.

Sequence in context: A057222 A124641 A169793 * A000395 A005325 A099623

Adjacent sequences: A054454 A054455 A054456 * A054458 A054459 A054460

Keyword

easy,nonn

Author

Wolfdieter Lang, Apr 27 2000

Status

approved