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

0,4

Links

Table of n, a(n) for n=0..25.

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.: (1-6*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

Prog

(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

Crossrefs

Essentially the same as A025230.

Sequence in context: A317629 A081912 A081188 * A154623 A196834 A005389

Adjacent sequences: A218183 A218184 A218185 * A218187 A218188 A218189

Keyword

nonn

Author

N. J. A. Sloane, Oct 23 2012

Extensions

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

Status

approved