A095152 Number of 3-block covers of a labeled n-set.

1, 32, 321, 2560, 18881, 135072, 954241, 6705920, 47020161, 329377312, 2306349761, 16146574080, 113032395841, 791245902752, 5538778714881, 38771623191040, 271401878897921, 1899814701967392, 13298707562817601, 93090966886860800, 651636810049438401

Offset: 2

Author

Vladeta Jovovic, May 31 2004

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (11,-31,21).

Crossrefs

Column of A055154.

Programs

Magma

[(11-6*3^n+7^n)/6 : n in [2..30]]; // Wesley Ivan Hurt, Aug 26 2014

Maple

seq((11-6*3^n+7^n)/6, n=2..50); # Robert Israel, Aug 25 2014

Mathematica

nn = 19; Table[Sum[(-1)^i Binomial[n, i] Binomial[2^(n - i) - 1, 3], {i, 0, n}], {n, 2, nn}] (* Geoffrey Critzer, Aug 24 2014 *)
Table[(11 - 6*3^n + 7^n)/6, {n, 2, 20}] (* Wesley Ivan Hurt, Aug 26 2014 *)

Formula

a(n) = (1/3!)*(11-6*3^n+7^n).

a(n) = 11*a(n-1)-31*a(n-2)+21*a(n-3). G.f.: -x^2*(21*x+1) / ((x-1)*(3*x-1)*(7*x-1)). - Colin Barker, Jul 12 2013

a(n) = sum(i=0..n, (-1)^i * C(n,i) * C(2^(n-i)-1,3) ). - Geoffrey Critzer, Aug 24 2014

Extensions

More terms from Colin Barker, Jul 12 2013