A218183 Number of true entries in truth tables of bracketed formulas connected by modified implication (case 3).

0, 0, 1, 4, 19, 108, 646, 4056, 26355, 175628, 1193906, 8246856, 57716798, 408391736, 2916689516, 20997741104, 152218453443, 1110202813836, 8140864778810, 59981252880360, 443834410644618, 3296876425605992, 24575508928455572, 183773880824034512

Offset

0,4

Links

Table of n, a(n) for n=0..23.

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. (see Proposition 6.4).

G.f.: (-5 + 3*sqrt(1-8*x) + 3*sqrt(3-4*x-2*sqrt(1-8*x)) + 4*x - sqrt(1-8*x)*sqrt(3-4*x-2*sqrt(1-8*x)))/4. - Michel Marcus, Jun 10 2021

Prog

(PARI) all_a(m) = {x= y+O(y^(m+1)); P = (-5 + 3*sqrt(1-8*x)+3*sqrt(3-4*x-2*sqrt(1-8*x)) + 4*x - sqrt(1-8*x)*sqrt(3-4*x-2*sqrt(1-8*x)))/4; for (n=0, m, print1(polcoeff(P, n, y), ", ")); } \\ Michel Marcus, Feb 17 2013
(PARI) concat(vector(2), Vec((-5 + 3*sqrt(1-8*x) + 3*sqrt(3-4*x-2*sqrt(1-8*x)) + 4*x - sqrt(1-8*x)*sqrt(3-4*x-2*sqrt(1-8*x)))/4 + O(x^20))) \\ Felix Fröhlich, Jun 10 2021

Crossrefs

Cf. A218184.

Sequence in context: A174992 A182541 A241839 * A206227 A091643 A323620

Adjacent sequences: A218180 A218181 A218182 * A218184 A218185 A218186

Keyword

nonn

Author

N. J. A. Sloane, Oct 23 2012

Extensions

More terms from Michel Marcus, Feb 17 2013

Status

approved