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
KEYWORD
easy,sign
AUTHOR
Paul Barry, Oct 16 2006
STATUS
approved