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A114220
a(n) = Sum_{k=0..floor(n/2)} (k - (k-1)*0^(n-2*k)).
14
1, 0, 1, 1, 2, 3, 4, 6, 7, 10, 11, 15, 16, 21, 22, 28, 29, 36, 37, 45, 46, 55, 56, 66, 67, 78, 79, 91, 92, 105, 106, 120, 121, 136, 137, 153, 154, 171, 172, 190, 191, 210, 211, 231, 232, 253, 254, 276, 277, 300, 301, 325, 326, 351, 352, 378, 379, 406, 407, 435, 436
OFFSET
0,5
COMMENTS
Diagonal sums of A114219.
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
Column k=2 of A309049 (for n>0).
Sequence in context: A049995 A294848 A055802 * A134519 A101505 A259625
KEYWORD
easy,nonn,changed
AUTHOR
Paul Barry, Nov 18 2005
STATUS
approved