|
|
A186940
|
|
Diagonal sums of number triangle A114709.
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|