A227792 Expansion of (1 + 6*x + 17*x^2 - x^3 - 3*x^4)/(1 - 6*x^2 + x^4).

1, 6, 23, 35, 134, 204, 781, 1189, 4552, 6930, 26531, 40391, 154634, 235416, 901273, 1372105, 5253004, 7997214, 30616751, 46611179, 178447502, 271669860, 1040068261, 1583407981, 6061962064, 9228778026, 35331704123, 53789260175, 205928262674

Offset: 0

Author

Ralf Stephan, Sep 23 2013

Keywords

• nonn
• easy

Comments

Also, values i where A067060(i)/i reaches a new maximum (conjectured).

Links

• E. I. Emerson, Recurrent Sequences in the Equation DQ^2=R^2+N, Fib. Quart., 7 (1969), pp. 231-242.
• Index entries for linear recurrences with constant coefficients, signature (0,6,0,-1)

Crossrefs

Cf. A041017.

Programs

Mathematica

CoefficientList[Series[(1+6x+17x^2-x^3-3x^4)/(1-6x^2+x^4),{x,0,40}],x] (* or *) LinearRecurrence[{0,6,0,-1},{1,6,23,35,134},40] (* Harvey P. Dale, Jun 12 2021 *)

PARI

a(n)=polcoeff((-3*x^4-x^3+17*x^2+6*x+1)/(x^4-6*x^2+1)+O(x^100),n)

Formula

G.f.: (1+6*x+17*x^2-x^3-3*x^4)/((1+2*x-x^2)*(1-2*x-x^2)).

a(2n) = A038723(n+1), n>0.

a(2n+1) = A001109(n+2).

a(n) = (1/4) * (A135532(n+3) + (-1)^n*A001333(n+2) ).