A218186 Number of rows with the value true in the truth tables of all bracketed formulas with n distinct propositions p_1, ..., p_n connected by the binary connective of m-implication (case 1).

0, 0, 1, 6, 37, 234, 1514, 9996, 67181, 458562, 3172478, 22206420, 157027938, 1120292388, 8055001716, 58314533400, 424740506109, 3110401363122, 22888001498102, 169155516667524, 1255072594261142, 9345400450314924, 69812926066668044, 523072984217339304, 3929809142578361938, 29598511892723647860

Offset: 0

Author

N. J. A. Sloane, Oct 23 2012

Keywords

• nonn

Links

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

Crossrefs

Essentially the same as A025230.

Programs

PARI

my(x='x+O('x^30)); concat([0,0], Vec((1-6*x-sqrt((1-4*x)*(1-8*x)))/2)) \\ Michel Marcus, Oct 21 2020

Formula

Yildiz gives a g.f.

G.f.: (1-6*x-sqrt((1-4*x)*(1-8*x)))/2. - Michel Marcus, Oct 21 2020

D-finite with recurrence n*a(n) +(n+5)*a(n-1) +(n+44)*a(n-2) +(n+331)*a(n-3) +10*(-902*n+3859)*a(n-4) +34720*(n-6)*a(n-5)=0. - R. J. Mathar, Nov 22 2023

Extensions

a(6) corrected by Georg Fischer, Jun 07 2021