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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 18 2016
STATUS
approved