A054457 - OEIS

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

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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.

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)

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

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