A123879 Expansion of (1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4).

1, 1, 0, -3, -7, -7, 5, 32, 57, 33, -95, -311, -416, -11, 1209, 2745, 2573, -2368, -12943, -22015, -11007, 40593, 123712, 157165, -14279, -498119, -1075179, -934944, 1090985, 5220257, 8476193, 3535193, -17205600

Offset

0,4

Comments

Row sums of number triangle A123878.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-5,3,-1).

Formula

a(n) = Sum_{k=0..n} Sum_{j=0..n} (-1)^(j-k)*C(n+j,2*j)*C(j+k,2*k).

Maple

seq(coeff(series((1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4), x, n+1), x, n), n = 0 .. 40); # G. C. Greubel, Aug 08 2019

Mathematica

LinearRecurrence[{3, -5, 3, -1}, {1, 1, 0, -3}, 40] (* G. C. Greubel, Aug 08 2019 *)

Prog

(PARI) my(x='x+O('x^40)); Vec((1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4)) \\ G. C. Greubel, Aug 08 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4) )); // G. C. Greubel, Aug 08 2019
(Sage)
def A123879_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4)).list()
A123879_list(40) # G. C. Greubel, Aug 08 2019
(GAP) a:=[1, 1, 0, -3];; for n in [5..40] do a[n]:=3*a[n-1]-5*a[n-2]+3*a[n-3]-a[n-4]; od; a; # G. C. Greubel, Aug 08 2019

Crossrefs

Cf. A123878, A123880.

Sequence in context: A197476 A246848 A019634 * A193016 A349604 A325894

Adjacent sequences: A123876 A123877 A123878 * A123880 A123881 A123882

Keyword

easy,sign

Author

Paul Barry, Oct 16 2006

Status

approved