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

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

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

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 *)

Crossrefs

Cf. A114709.

Hankel transform is A186941.

Sequence in context: A154135 A182274 A103091 * A376311 A101751 A374876

Adjacent sequences: A186937 A186938 A186939 * A186941 A186942 A186943

Keyword

nonn,easy

Author

Paul Barry, Mar 01 2011

Extensions

More terms from Vincenzo Librandi, Feb 14 2014

Status

approved