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A095153 Number of 4-block covers of a labeled n-set. 1

%I #27 Mar 18 2024 16:46:51

%S 35,1225,24990,426650,6779185,104394675,1585021340,23909487700,

%T 359582866335,5400330984125,81051093085690,1216089331752750,

%U 18243600636165485,273669834496409575,4105158293128058040,61578149829707541800,923677675484159636635

%N Number of 4-block covers of a labeled n-set.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (26,-196,486,-315).

%F a(n) = (1/4!)*(-50+35*3^n-10*7^n+15^n).

%F G.f.: 35*x^3*(9*x+1) / ((x-1)*(3*x-1)*(7*x-1)*(15*x-1)). - _Colin Barker_, Jul 13 2013

%F a(n) = Sum_{i=0..n} (-1)^i * C(n,i) * C(2^(n-i)-1,4). - _Geoffrey Critzer_, Aug 24 2014

%F a(n) = 26*a(n-1)-196*a(n-2)+486*a(n-3)-315*a(n-4). - _Wesley Ivan Hurt_, Aug 26 2014

%p A095153:=n->(-50+35*3^n-10*7^n+15^n)/24: seq(A095153(n), n=3..20); # _Wesley Ivan Hurt_, Aug 26 2014

%t nn = 19; Table[Sum[(-1)^i Binomial[n, i] Binomial[2^(n - i) - 1, 4], {i, 0, n}], {n, 3, nn}] (* _Geoffrey Critzer_, Aug 24 2014 *)

%t Table[(-50 + 35*3^n - 10*7^n + 15^n)/24, {n, 3, 20}] (* _Wesley Ivan Hurt_, Aug 26 2014 *)

%o (Magma) [(-50 + 35*3^n - 10*7^n + 15^n)/24 : n in [3..20]]; // _Wesley Ivan Hurt_, Aug 26 2014

%Y Column of A055154.

%K easy,nonn,changed

%O 3,1

%A _Vladeta Jovovic_, May 31 2004

%E More terms from _Colin Barker_, Jul 13 2013

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)