A095155 Number of 6-block covers of a labeled n-set.

7, 4977, 711326, 63602770, 4709047749, 320401872035, 20951777849212, 1344192783541860, 85442420316605891, 5406486257577661333, 341342273242841583258, 21527330224106110255670, 1356927944579525164818433, 85508356311211819638169671, 5387705299223777670172444664

Offset

3,1

Links

Table of n, a(n) for n=3..17.

Index entries for linear recurrences with constant coefficients, signature (120,-4593,69688,-428787,978768,-615195).

Formula

a(n) = (1/6!)*(-1764+1624*3^n-735*7^n+175*15^n-21*31^n+63^n).

G.f.: 7*x^3*(87885*x^3+20891*x^2+591*x+1) / ((x-1)*(3*x-1)*(7*x-1)*(15*x-1)*(31*x-1)*(63*x-1)). - Colin Barker, Jul 12 2013

a(n) = sum(i=0..n, (-1)^i * C(n,i) * C(2^(n-i)-1,6) ). - Geoffrey Critzer, Aug 24 2014

a(n) = 120*a(n-1)-4593(n-2)+69688*a(n-3)-428787*a(n-4)+978768*a(n-5)-615195*a(n-6). - Wesley Ivan Hurt, Aug 26 2014

Maple

A095155:=n->(-1764+1624*3^n-735*7^n+175*15^n-21*31^n+63^n)/720: seq(A095155(n), n=3..20); # Wesley Ivan Hurt, Aug 26 2014

Mathematica

nn = 19; Table[ Sum[(-1)^i Binomial[n, i] Binomial[2^(n - i) - 1, 6], {i, 0, n}], {n, 3, nn}] (* Geoffrey Critzer, Aug 24 2014 *)
Table[(-1764 + 1624*3^n - 735*7^n + 175*15^n - 21*31^n + 63^n)/720, {n, 3, 20}] (* Wesley Ivan Hurt, Aug 26 2014 *)

Prog

(Magma) [(-1764+1624*3^n-735*7^n+175*15^n-21*31^n+63^n)/720 : n in [3..20]]; // Wesley Ivan Hurt, Aug 26 2014

Crossrefs

Column of A055154.

Sequence in context: A103856 A364640 A340292 * A219893 A243780 A246519

Adjacent sequences: A095152 A095153 A095154 * A095156 A095157 A095158

Keyword

easy,nonn

Author

Vladeta Jovovic, May 31 2004

Extensions

More terms from Colin Barker, Jul 12 2013

Status

approved