A274295 a(n) = n+binomial(2*n-6,n-3)+binomial(2*n-5,n-3)+binomial(n-1,n-3)+Sum_{i=1..n-3} (binomial(n+i-3,n-3)+2*n-i-5).

1, 1, 3, 6, 16, 43, 120, 369, 1244, 4449, 16424, 61645, 233568, 890421, 3409866, 13105083, 50517580, 195234557, 756198408, 2934687173, 11408742152, 44420399805, 173191793402, 676104404123, 2642356839108, 10337529692357, 40481034411830, 158658210122079, 622329139387184, 2442857958597649

Offset

0,3

Comments

For n >= 5 this is the number of residuated maps from the lattice N_n to itself.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Erika D. Foreman, Order automorphisms on the lattice of residuated maps of some special nondistributive lattices, (2015). Univ. Louisville, Electronic Theses and Dissertations. Paper 2257.

Formula

G.f.: -11-12/(x - 1)^3 + x*(-4 + 31/(x-1)^3 + x*(1/sqrt(1 - 4*x) - 23/(x - 1)^3 + x/sqrt(1 - 4*x))). - Benedict W. J. Irwin, Aug 09 2016

a(n) ~ 5*4^(n-3)/sqrt(Pi*n). - Ilya Gutkovskiy, Aug 09 2016

Conjecture: (-n+2)*a(n) +(7*n-18)*a(n-1) +14*(-n+3)*a(n-2) +2*(3*n-2)*a(n-3) +(11*n-90)*a(n-4) +(-13*n+102)*a(n-5) +2*(2*n-17)*a(n-6)=0. - R. J. Mathar, Oct 07 2016

Maple

g:=n->n+binomial(2*n-6, n-3)+binomial(2*n-5, n-3)+binomial(n-1, n-3)+add((binomial(n+i-3, n-3)+2*n-i-5), i=1..n-3);
[seq(g(n), n=0..40)];

Mathematica

Table[n + Binomial[2 * n - 6, n - 3] + Binomial[2 * n - 5, n - 3] + Binomial[n - 1, n - 3] + Sum[(Binomial[n + i - 3, n - 3] + 2 * n - i - 5), {i, 1, n - 3}], {n, 0, 20}] (* Benedict W. J. Irwin, Aug 09 2016 *)
CoefficientList[Series[-11-12/(x - 1)^3 + x*(-4 + 31/(x-1)^3 + x*(1/Sqrt[1 - 4*x] - 23/(x - 1)^3 + x/Sqrt[1 - 4*x])), {x, 0, 50}], x] (* G. C. Greubel, Jun 05 2017 *)

Prog

(PARI) x='x+O('x^50); Vec(-11-12/(x - 1)^3 + x*(-4 + 31/(x-1)^3 + x*(1/sqrt(1 - 4*x) - 23/(x - 1)^3 + x/sqrt(1 - 4*x)))) \\ G. C. Greubel, Jun 05 2017

Crossrefs

Sequence in context: A202839 A371705 A007561 * A192676 A202846 A107269

Adjacent sequences: A274292 A274293 A274294 * A274296 A274297 A274298

Keyword

nonn

Author

N. J. A. Sloane, Jun 18 2016

Status

approved