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A060484 Number of 6-block tricoverings of an n-set. 5
1, 95, 3107, 75835, 1653771, 34384875, 700030507, 14116715435, 283432939691, 5679127043755, 113683003777707, 2274630646577835, 45502044971338411, 910133025632152235, 18203564201836161707, 364080180268471397035 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

COMMENTS

A covering of a set is a tricovering if every element of the set is covered by exactly three blocks of the covering.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 3..200

Index entries for linear recurrences with constant coefficients, signature (45,-720,5220,-17664,25920,-12800).

FORMULA

a(n) = (1/6!)*(20^n - 6*10^n - 15*8^n + 135*4^n - 310*2^n + 240).

E.g.f. for k-block tricoverings of an n-set is exp(-x+x^2/2+(exp(y)-1)*x^3/3)*Sum_{k=0..inf}x^k/k!*exp(-1/2*x^2*exp(k*y))*exp(binomial(k, 3)*y).

G.f.: -x^3*(800*x^3+448*x^2-50*x-1) / ((x-1)*(2*x-1)*(4*x-1)*(8*x-1)*(10*x-1)*(20*x-1)). - Colin Barker, Jan 12 2013

a(n) = 45*a(n-1)-720*a(n-2)+5220*a(n-3)-17664*a(n-4)+25920*a(n-5)-12800*a(n-6). - Wesley Ivan Hurt, Oct 18 2021

MATHEMATICA

With[{c=1/6!}, Table[c(20^n-6*10^n-15*8^n+135*4^n-310*2^n+240), {n, 3, 20}]] (* or *) LinearRecurrence[{45, -720, 5220, -17664, 25920, -12800}, {1, 95, 3107, 75835, 1653771, 34384875}, 20] (* Harvey P. Dale, Jan 05 2017 *)

PROG

(PARI) a(n) = (1/6!)*(20^n - 6*10^n - 15*8^n + 135*4^n - 310*2^n + 240) \\ Andrew Howroyd, Dec 15 2018

CROSSREFS

Column k=6 of A060487.

Cf. A006095, A060483, A060485, A060486, A060090-A060095, A060069, A060070, A060051-A060053, A002718, A059443, A003462, A059945-A059951.

Sequence in context: A055829 A243801 A093295 * A017811 A017758 A203342

Adjacent sequences:  A060481 A060482 A060483 * A060485 A060486 A060487

KEYWORD

nonn,easy

AUTHOR

Vladeta Jovovic, Mar 20 2001

STATUS

approved

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Last modified June 26 00:12 EDT 2022. Contains 354870 sequences. (Running on oeis4.)