A186940 Diagonal sums of number triangle A114709.
1, 0, 3, 6, 31, 126, 589, 2772, 13485, 66780, 336207, 1714698, 8841627, 46015002, 241394073, 1275137448, 6776728825, 36208438488, 194388488155, 1048061471886, 5672504958327, 30808982057046, 167864115588325, 917271225518076, 5025659929354981
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
Programs
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Mathematica
Rest[CoefficientList[Series[(1+3*x-2*x^2-Sqrt[1-6*x+x^2])/(2*(3+x-3*x^2+x^3)), {x, 0, 20}], x]] (* Vaclav Kotesovec, Feb 01 2014 *)
Formula
G.f. (for offset 1): (1+3*x-2*x^2-sqrt(1-6*x+x^2))/(2*(3+x-3*x^2+x^3)).
Conjecture: 3*(n+1)*a(n) +(10-17*n)*a(n-1) -6*(n+1)*a(n-2) +10*(2*n-1)*a(n-3) +9*(1-n)*a(n-4) +(n-2)*a(n-5) =0. - R. J. Mathar, Nov 17 2011
a(n) ~ sqrt(3*sqrt(2)-4) * (3+2*sqrt(2))^(n+2) / (36 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 01 2014
Extensions
More terms from Vincenzo Librandi, Feb 14 2014