A245923 G.f.: (1-x + sqrt(1 - 14*x + x^2)) / (2*(1 - 14*x + x^2)).

1, 10, 127, 1684, 22717, 309214, 4231675, 58117672, 800173945, 11037041074, 152448280183, 2107959984316, 29172777600565, 404016491894662, 5598523988234227, 77617624970307664, 1076533162210721521, 14936507761662251866, 207302489038473478255, 2877906561872502533860

Offset

0,2

Comments

Self-convolution of A245926.

Limit a(n+1)/a(n) = 7 + 4*sqrt(3).

Links

G. C. Greubel, Table of n, a(n) for n = 0..870

Formula

a(n) ~ (7+4*sqrt(3))^(n+1) * (2-sqrt(3))/8 * (1+1/(3^(1/4)*sqrt(Pi*n/2))). - Vaclav Kotesovec, Aug 17 2014

D-finite with recurrence: n*a(n) +7*(-4*n+3)*a(n-1) +99*(2*n-3)*a(n-2) +7*(-4*n+9)*a(n-3) +(n-3)*a(n-4)=0. - R. J. Mathar, Jan 23 2020

Example

G.f.: A(x) = 1 + 10*x + 127*x^2 + 1684*x^3 + 22717*x^4 + 309214*x^5 +...

Mathematica

CoefficientList[Series[(1 - x + Sqrt[1 - 14*x + x^2])/(2*(1 - 14*x + x^2)), {x, 0, 50}], x] (* G. C. Greubel, Feb 14 2017 *)

Prog

(PARI) {a(n)=polcoeff( (1-x + sqrt(1-14*x+x^2 +x*O(x^n))) / (2*(1-14*x+x^2 +x*O(x^n))), n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A245924, A245926.

Sequence in context: A192600 A079241 A270965 * A218474 A234284 A296379

Adjacent sequences: A245920 A245921 A245922 * A245924 A245925 A245926

Keyword

nonn

Author

Paul D. Hanna, Aug 16 2014

Status

approved