A094735 Number of connected 3-element multiantichains on a labeled n-set.

0, 1, 1, 8, 75, 796, 8051, 73788, 623155, 4965836, 38028051, 283400668, 2072874035, 14966280876, 107083717651, 761327161148, 5388524417715, 38017832427916, 267623218488851, 1880883687651228, 13203904989574195, 92616374066478956, 649261556308773651

Offset

0,4

Links

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

Index entries for linear recurrences with constant coefficients, signature (22,-190,820,-1849,2038,-840).

Formula

E.g.f.: (1/3!)*(exp(7*x) - 6*exp(5*x) + 3*exp(4*x) + 20*exp(3*x) - 39*exp(2*x) + 35*exp(x) - 14).

G.f.: -x*(1960*x^5 - 1695*x^4 + 731*x^3 - 176*x^2 + 21*x - 1) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(7*x-1)). - Colin Barker, Jul 13 2013

a(n) = (7^n - 6*5^n + 20*3^n + 3*4^n - 39*2^n + 35)/6, n > 0. - Benedict W. J. Irwin, May 25 2016

Mathematica

Table[(7^n-6*5^n+20*3^n+3*4^n-39*2^n+35)/6(1-UnitStep[-n]), {n, 0, 20}] (* Benedict W. J. Irwin, May 25 2016 *)

Prog

(PARI) x='x+O('x^50); concat([0], Vec(serlaplace((1/3!)*(exp(7*x) - 6*exp(5*x) + 3*exp(4*x) + 20*exp(3*x) - 39*exp(2*x) + 35*exp(x) - 14)))) \\ G. C. Greubel, Oct 08 2017

Crossrefs

Cf. A094033-A094037, A094729-A094738.

Sequence in context: A145600 A268085 A231617 * A067306 A361528 A261065

Adjacent sequences: A094732 A094733 A094734 * A094736 A094737 A094738

Keyword

nonn,easy

Author

Goran Kilibarda, Vladeta Jovovic, May 24 2004

Extensions

More terms from Colin Barker, Jul 13 2013

Status

approved