A092794 Number of connected relations.
1, 21, 265, 2733, 25441, 223461, 1895545, 15736413, 128882641, 1046542101, 8451838825, 68020609293, 546227922241, 4380272835141, 35094966838105, 281025802973373, 2249545355064241, 18003091856638581, 144058517372685385, 1152637601335180653
Offset: 1
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
- G. Kilibarda and V. Jovovic, Enumeration of some classes of T_0-hypergraphs, arXiv:1411.4187 [math.CO], 2014.
- Index entries for linear recurrences with constant coefficients, signature (17,-92,160).
Programs
-
Mathematica
CoefficientList[Series[-x*(4*x + 1)/((4*x - 1)*(5*x - 1)*(8*x - 1)), {x, 0, 50}], x] (* G. C. Greubel, Oct 05 2017 *) -
PARI
x='x+O('x^50); Vec(x*(4*x+1)/((1-4*x)*(1-5*x)*(1-8*x))) \\ G. C. Greubel, Oct 05 2017
Formula
a(n) = 8^n - 3*5^n + 2*4^n.
From Colin Barker, Jul 13 2013: (Start)
a(n) = 17*a(n-1) - 92*a(n-2) + 160*a(n-3).
G.f.: x*(4*x+1) / ((1-4*x)*(1-5*x)*(1-8*x)). (End)
Extensions
Additional term from Colin Barker, Jul 13 2013