A396155 - OEIS

%I #10 Jun 05 2026 20:59:21

%S 0,0,0,0,0,0,1,11,96,756,5616,40176,279936,1912891,12876971,85659426,

%T 564341256,3688350336,23943886416,154545830496,992568888601,

%U 6347169767231,40433515229136,256703819205816,1624837770706896,10256706688151376,64586266099808256,405793425954721411,2544413573081381591

%N a(n) is the number of possible outcomes having a run of 6 or more sixes when a die is rolled n times.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (11,-25,-25,-25,-25,-25,-30).

%F G.f.: x^6/((6*x - 1)*(5*x^6 + 5*x^5 + 5*x^4 + 5*x^3 + 5*x^2 + 5*x - 1)).

%F a(n) = A396158(n,6).

%t LinearRecurrence[{11, -25, -25, -25, -25, -25, -30}, {0, 0, 0, 0, 0, 0, 1}, 30] (* _Amiram Eldar_, May 26 2026 *)

%o (PARI) concat([0, 0, 0, 0, 0, 0], Vec(x^6/((6*x-1)*(5*x^6+5*x^5+5*x^4+5*x^3+5*x^2+5*x-1)) + O(x^29)))

%Y Cf. A396158.

%Y Cf. A000040, A005062, A395827, A396152, A396153, A396154, A396156.

%K nonn,easy

%O 0,8

%A _A.H.M. Smeets_, May 26 2026