OFFSET
0,5
COMMENTS
Row sums of number triangle A099569.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-2,-1).
FORMULA
a(n) = 2*0^n + (-1)^n*(n-2) - Sum_{k=0..n} k*binomial(n, k)*(-1)^(n-k).
a(n) = -2*a(n-1) - a(n-2), n>3, with a(0) = 1, a(1) = 0, a(2) = 0, a(3) = -1.
From G. C. Greubel, Jul 25 2022: (Start)
a(n) = (-1)^n*(n-2) - [n=1] + 3*[n=0].
a(n) = A038608(n-2), for n >= 2, with a(0) = 1, a(1) = 0.
E.g.f.: 3 - x - (x+2)*exp(-x). (End)
MATHEMATICA
Table[(-1)^n*(n-2) -Boole[n==1]+3*Boole[n==0], {n, 0, 100}] (* G. C. Greubel, Jul 25 2022 *)
PROG
(Magma) [1, 0] cat [(-1)^n*(n-2): n in [2..100]]; // G. C. Greubel, Jul 25 2022
(SageMath) [(-1)^n*(n-2) -bool(n==1) +3*bool(n==0) for n in (0..100)] # G. C. Greubel, Jul 25 2022
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Oct 22 2004
STATUS
approved