A249312 Expansion of x*(1+11*x-10*x^3)/(1-12*x^2+10*x^4).

1, 11, 12, 122, 134, 1354, 1488, 15028, 16516, 166796, 183312, 1851272, 2034584, 20547304, 22581888, 228054928, 250636816, 2531186096, 2781822912, 28093683872, 30875506784, 311812345504, 342687852288, 3460811307328, 3803499159616, 38411612232896

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(26)-4).

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 (0,12,0,-10).

Crossrefs

Cf. A007068 (k=1), A022165 (k=2), A249310 (k=3), A249311 (k=4), A249313 (k=6).

Programs

Mathematica

LinearRecurrence[{0,12,0,-10},{1,11,12,122},40] (* Harvey P. Dale, Feb 02 2015 *)

PARI

Vec(x*(1+11*x-10*x^3)/(1-12*x^2+10*x^4) + O(x^100))

Formula

a(1)=1, a(2)=11, a(3)=12, a(4)=122, a(n)=12*a(n-2)-10*a(n-4). - Harvey P. Dale, Feb 02 2015