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

Author

Paul Barry, Oct 16 2006

Keywords

• easy
• sign

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).

Crossrefs

Cf. A123878, A123880.

Programs

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

Magma

R:=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

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 *)

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

Sage

def A123879_list(prec):
    P. = 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

Formula

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