A095154 Number of 5-block covers of a labeled n-set.

21, 2919, 155106, 6054006, 208493607, 6791135085, 215553311652, 6758354401932, 210657488261913, 6547648042583571, 203236346721890118, 6304217491485837378, 195489116558570607339, 6061038320388658194777, 187905324183802270088904, 5825262097993829801550744

Offset: 3

Author

Vladeta Jovovic, May 31 2004

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (57,-1002,6562,-15381,9765).

Crossrefs

Column of A055154.

Programs

Magma

[(274-225*3^n+85*7^n-15*15^n+31^n)/120 : n in [3..20]]; // Wesley Ivan Hurt, Aug 25 2014

Maple

A095154:=n->(274-225*3^n+85*7^n-15*15^n+31^n)/120: seq(A095154(n), n=3..20); # Wesley Ivan Hurt, Aug 25 2014

Mathematica

nn = 19; Table[Sum[(-1)^i Binomial[n, i] Binomial[2^(n - i) - 1, 5], {i, 0, n}], {n, 3, nn}] (* Geoffrey Critzer, Aug 24 2014 *)
Table[(274 - 225*3^n + 85*7^n - 15*15^n + 31^n)/120, {n, 3, 20}] (* Wesley Ivan Hurt, Aug 25 2014 *)

Formula

a(n) = (1/5!)*(274-225*3^n+85*7^n-15*15^n+31^n).

G.f.: -21*x^3*(465*x^2+82*x+1) / ((x-1)*(3*x-1)*(7*x-1)*(15*x-1)*(31*x-1)). - Colin Barker, Jul 13 2013

a(n) = Sum_{i=0..n} (-1)^i * C(n,i) * C(2^(n-i)-1,5). - Geoffrey Critzer, Aug 24 2014

a(n) = 57*a(n-1)-1002*a(n-2)+6562*a(n-3)-15381*a(n-4)+9765*a(n-5). - Wesley Ivan Hurt, Aug 25 2014

Extensions

More terms from Colin Barker, Jul 13 2013