OFFSET
0,3
COMMENTS
Diagonal sums of number triangle A110522.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-2,0,-2)
FORMULA
a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..(n-k)} (-1)^(n-k-j)*C(n-k, j) *(-3)^(j-k)*C(k, j-k).
a(n) = (-1)^n * A077999(n). - G. C. Greubel, Jun 27 2019
MATHEMATICA
CoefficientList[Series[(1+x)/(1+2*x+2*x^3), {x, 0, 40}], x] (* G. C. Greubel, Aug 30 2017 *)
LinearRecurrence[{-2, 0, -2}, {1, -1, 2}, 40] (* G. C. Greubel, Jun 27 2019 *)
PROG
(PARI) my(x='x+O('x^40)); Vec((1+x)/(1+2*x+2*x^3)) \\ G. C. Greubel, Aug 30 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)/( 1+2*x+2*x^3) )); // G. C. Greubel, Jun 27 2019
(Sage) ((1+x)/(1+2*x+2*x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jun 27 2019
(GAP) a:=[1, -1, 2];; for n in [4..40] do a[n]:=-2*(a[n-1]+a[n-3]); od; a; # G. C. Greubel, Jun 27 2019
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Jul 24 2005
STATUS
approved