A249313 Expansion of x*(1+13*x-12*x^3)/(1-14*x^2+12*x^4).

1, 13, 14, 170, 184, 2224, 2408, 29096, 31504, 380656, 412160, 4980032, 5392192, 65152576, 70544768, 852375680, 922920448, 11151428608, 12074349056, 145891492352, 157965841408, 1908663749632, 2066629591040, 24970594586624, 27037224177664, 326684359217152

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(37)-5).

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 (0,14,0,-12).

Crossrefs

Cf. A007068 (k=1), A022165 (k=2), A249310 (k=3), A249311 (k=4), A249312 (k=5).

Programs

Mathematica

CoefficientList[Series[x (1+13x-12x^3)/(1-14x^2+12x^4),{x,0,30}],x] (* or *) LinearRecurrence[{0,14,0,-12},{1,13,14,170},30] (* Harvey P. Dale, Oct 19 2018 *)

PARI

Vec(x*(1+13*x-12*x^3)/(1-14*x^2+12*x^4) + O(x^100))