A249310 Expansion of x*(1+7*x-6*x^3)/(1-8*x^2+6*x^4).

1, 7, 8, 50, 58, 358, 416, 2564, 2980, 18364, 21344, 131528, 152872, 942040, 1094912, 6747152, 7842064, 48324976, 56167040, 346116896, 402283936, 2478985312, 2881269248, 17755181120, 20636450368, 127167537088, 147803987456, 910809209984, 1058613197440

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(10)-2).

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

• Vincenzo Librandi, 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 (0,8,0,-6).

Crossrefs

Cf. A007068 (k=1), A022165 (k=2), A249311 (k=4), A249312 (k=5), A249313 (k=6).

Programs

Mathematica

CoefficientList[Series[(1 + 7 x - 6 x^3)/(1 - 8 x^2 + 6 x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 25 2014 *)
LinearRecurrence[{0,8,0,-6},{1,7,8,50},30] (* Harvey P. Dale, Sep 22 2019 *)

PARI

Vec((1+7*x-6*x^3)/(1-8*x^2+6*x^4) + O(x^100))