OFFSET
0,5
COMMENTS
Diagonal sums of A114219.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1)
FORMULA
G.f.: (1-x-x^2+2x^3)/((1-x)*(1-x^2)^2).
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
a(n) = (2*n^2-2*n+7 + (9-2*n)*(-1)^n)/16.
a(n) = A055802(n+1), n > 1. - R. J. Mathar, Aug 11 2008
E.g.f.: (1/16)*((9 + 2*x)*exp(-x) + (7 + 2*x^2)*exp(x)). - G. C. Greubel, Oct 21 2024
MATHEMATICA
CoefficientList[Series[(1-x-x^2+2x^3)/((1-x)(1-x^2)^2), {x, 0, 80}], x] (* Harvey P. Dale, Mar 24 2011 *)
PROG
(Magma) [(2*n^2-2*n+7 + (9-2*n)*(-1)^n)/16: n in [0..80]]; // G. C. Greubel, Oct 21 2024
(SageMath)
def A114220(n): return (2*n^2-2*n+7 + (9-2*n)*(-1)^n)//16
[A114220(n) for n in range(81)] # G. C. Greubel, Oct 21 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Nov 18 2005
STATUS
approved