A249311 Expansion of x*(1+9*x-8*x^3)/(1-10*x^2+8*x^4).

1, 9, 10, 82, 92, 748, 840, 6824, 7664, 62256, 69920, 567968, 637888, 5181632, 5819520, 47272576, 53092096, 431272704, 484364800, 3934546432, 4418911232, 35895282688, 40314193920, 327476455424, 367790649344, 2987602292736, 3355392942080, 27256211283968

Offset: 1

Author

Colin Barker, Oct 25 2014

Keywords

• nonn
• easy

Comments

It seems that this is also the first row of the spectral array W(sqrt(17)-3).

It also seems that, for all k>0, the first row of W(sqrt(k^2+1)-k+1) has a generating function of the form x*(1+(2*k+1)*x-2*k*x^3)/(1-(2*k+2)*x^2+2*k*x^4).

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• A. Fraenkel and C. Kimberling, Generalized Wythoff arrays, shuffles and interspersions, Discrete Mathematics 126 (1994) 137-149.
• Index entries for linear recurrences with constant coefficients, signature (0,10,0,-8).

Crossrefs

Cf. A007068 (k=1), A022165 (k=2), A249310 (k=3), A249312 (k=5), A249313 (k=6).

Programs

PARI

Vec(x*(1+9*x-8*x^3)/(1-10*x^2+8*x^4) + O(x^100))