A113859 Expansion of (7-14*x+6*x^2)/((1-x)*(2*x^2-4*x+1)); related to the binomial transform of Pell numbers A000129 (see formula and comment for A007070).

7, 21, 69, 233, 793, 2705, 9233, 31521, 107617, 367425, 1254465, 4283009, 14623105, 49926401, 170459393, 581984769, 1987020289, 6784111617, 23162405889, 79081400321, 270000789505, 921840357377, 3147359850497, 10745758687233

Offset

0,1

Comments

If g.f. (x^6+5*x^4+6*x^2+1)/(x^7+6*x^5+10*x^3+4*x) is expanded, where (x^6+5*x^4+6*x^2+1) and (x^7+6*x^5+10*x^3+4*x) are the 7th and 8th Fibonacci polynomials, respectively, the sequence: [0, 7/8, 0, -21/16, 0, 69/32, 0, -233/64, 0, 793/128, 0, -2705/256, ] is returned. (a(n)) is seen to be the numerators of the bisection of this sequences, apart from signs.

Links

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

Formula

a(n+1) - a(n) = A007070(n+2), a(n) - 2*a(n+1) + a(n+2) = A007052(n+3) (Number of order consecutive partitions of n), a(n+3) - 3*a(n+2) + 3*a(n+1) - a(n) = A003480(n+4), a(n+2) - a(n) = A111567(n+3)

Maple

with(combinat, fibonacci): seq(fibonacci(i, x), i=1..15); [[generates sequence of Fibonacci polynomials]]

Crossrefs

Cf. A007070, A007052, A003480, A111567, A000129.

Sequence in context: A005032 A152766 A152671 * A245404 A215494 A146533

Adjacent sequences: A113856 A113857 A113858 * A113860 A113861 A113862

Keyword

easy,nonn

Author

Creighton Dement, Jan 25 2006

Status

approved