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A073381 Fourth convolution of A000129(n+1) (generalized (2,1)-Fibonacci, called Pell numbers), n>=0, with itself. 1
1, 10, 65, 340, 1555, 6482, 25235, 93200, 330070, 1129580, 3756950, 12197320, 38787770, 121148300, 372476410, 1129367632, 3382133695, 10016694470, 29370557375, 85341915260, 245939376949, 703423066190 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

M. Janjic, Hessenberg Matrices and Integer Sequences , J. Int. Seq. 13 (2010) # 10.7.8.

Index entries for linear recurrences with constant coefficients, signature (10,-35,40,30,-68,-30,40,35,10,1).

FORMULA

a(n) = sum(b(k) * c(n-k), k=0..n) with b(k) := A000129(k+1) and c(k) := A073380(k).

a(n) = sum((2^n) * binomial(n-k+4, 4) * binomial(n-k, k) * (1/4)^k, k=0..floor(n/2)).

a(n)= ((2457+2128*n+572*n^2+48*n^3)*(n+1)*U(n+1)+5*(123+142*n+44*n^2+4*n^3) *(n+2)*U(n))/(3*2^11), with U(n) := A000129(n+1), n>=0.

G.f.: 1/(1-(2+x)*x)^5.

a(n) = F''''(n+5, 2)/4!, that is, 1/4! times the 4th derivative of the (n+5)th Fibonacci polynomial evaluated at x=2. - T. D. Noe, Jan 19 2006

CROSSREFS

Fifth (m=4) column of triangle A054456, A073380.

Sequence in context: A160458 A023009 A169797 * A092441 A022638 A003519

Adjacent sequences:  A073378 A073379 A073380 * A073382 A073383 A073384

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 02 2002

STATUS

approved

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Last modified October 19 00:36 EDT 2018. Contains 316327 sequences. (Running on oeis4.)