A094734 Number of connected 2-element multiantichains on a labeled n-set.
0, 1, 1, 4, 19, 76, 271, 904, 2899, 9076, 27991, 85504, 259579, 784876, 2366911, 7125304, 21425059, 64373476, 193317031, 580344304, 1741819339, 5227030876, 15684238351, 47059006504, 141189602419, 423593973076, 1270832250871, 3812597415904, 11437993574299
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6,-11,6).
Programs
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Mathematica
Join[{0},LinearRecurrence[{6,-11,6},{1,1,4},30]] (* Harvey P. Dale, Nov 28 2014 *) -
PARI
x='x+O('x^50); concat([0], Vec(serlaplace((1/2!)*(exp(3*x) - 3*exp(2*x) + 5*exp(x) - 3)))) \\ G. C. Greubel, Oct 07 2017
Formula
E.g.f.: (1/2!)*(exp(3*x) - 3*exp(2*x) + 5*exp(x) - 3).
From Colin Barker, Jul 13 2013: (Start)
a(n) = (5 - 3*2^n + 3^n)/2 for n > 0.
a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n > 3.
G.f.: -x*(9*x^2-5*x+1)/((x-1)*(2*x-1)*(3*x-1)). (End)
Extensions
More terms from Colin Barker, Jul 13 2013