A218182 Number of truth tables of bracketed formulas (case 1).

0, 0, 1, 6, 33, 194, 1198, 7676, 50581, 340682, 2335186, 16237284, 114255994, 812107412, 5822171548, 42052209400, 305714145869, 2235262899418, 16426616425002, 121265916776148, 898878250833358, 6687497426512700, 49920590244564484

Offset

0,4

Links

Table of n, a(n) for n=0..22.

Volkan Yildiz, General combinatorical structure of truth tables of bracketed formulas connected by implication, arXiv preprint arXiv:1205.5595 [math.CO], 2012.

Formula

Yildiz gives a g.f.

G.f.: ((1-8*x)^(1/2)-3)*((2+2*(1-8*x)^(1/2)+8*x)^(1/2)-2)/8. - Mark van Hoeij, May 16 2013

D-finite with recurrence n*(2*n-1)*(n-1)*a(n) -2*(n-1)*(11*n^2-27*n+15)*a(n-1) +8*(-3*n^3+42*n^2-149*n+155)*a(n-2) +32*(2*n-7)*(8*n^2-53*n+85)*a(n-3) +128*(n-5)*(2*n-7)*(2*n-9)*a(n-4)=0. - R. J. Mathar, Dec 03 2025

Prog

(PARI) my(x='x+O('x^30)); concat([0, 0], Vec(((1-8*x)^(1/2)-3)*((2+2*(1-8*x)^(1/2)+8*x)^(1/2)-2)/8)) \\ Michel Marcus, Oct 21 2020

Crossrefs

Cf. A186997, A218045.

Sequence in context: A379139 A286187 A260774 * A093964 A391278 A361776

Adjacent sequences: A218179 A218180 A218181 * A218183 A218184 A218185

Keyword

nonn

Author

N. J. A. Sloane, Oct 23 2012

Status

approved