OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-2,-3,-2,-1).
FORMULA
G.f.: (1 -2*x -2*x^2 -x^3)/(1 +x +x^2)^2.
a(n) = Sum_{k=0..n} (-1)^(n-k+1)*(n+k+2)*binomial(n+k+1, 2*k). - Paul Barry, Apr 19 2010
a(n) = 2*floor(n/3) + 1 if (n mod 3) = 0, -4*(floor(n/3) + 1) if (n mod 3) = 1 and 2*floor(n/3) + 3 if (n mod 3) = 2. - G. C. Greubel, Jun 16 2021
MATHEMATICA
a[n_]:= a[n]= Sum[(-1)^(n-k+1)*(n+k+2)*Binomial[n+k+1, 2*k], {k, 0, n+1}];
Table[a[n], {n, 0, 65}] (* G. C. Greubel, Jun 16 2021 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 65); Coefficients(R!( (1-2*x-2*x^2-x^3)/(1+x+x^2)^2 )); // G. C. Greubel, Jun 16 2021
(Sage)
@CachedFunction
def A138187(n):
if (n%3==0): return 2*(n//3) +1
elif (n%3==1): return -4*((n//3) +1)
else: return 2*(n//3) +3
[A138187(n) for n in (0..65)] # G. C. Greubel, Jun 16 2021
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Mar 04 2008
STATUS
approved