A396154 - OEIS

%I #6 May 25 2026 18:56:24

%S 0,0,0,0,0,1,11,96,756,5616,40176,279931,1912811,12876066,85650696,

%T 564264576,3687717456,23938890361,154507689791,992285228496,

%U 6345103937976,40418727227856,256599474317136,1624110448674691,10251689936941271,64551976895557626,405560928053970756

%N a(n) is the number of possible outcomes having a run of 5 or more sixes when a die is rolled n times.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (11,-25,-25,-25,-25,-30).

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

%F a(n) = A396158(n,5).

%t LinearRecurrence[{11, -25, -25, -25, -25, -30},{0, 0, 0, 0, 0, 1}, 27] (* _Amiram Eldar_, May 20 2026 *)

%o (PARI) concat([0, 0, 0, 0, 0], Vec(x^5/((6*x-1)*(5*x^5+5*x^4+5*x^3+5*x^2+5*x-1)) + O(x^27)))

%Y Cf. A396158.

%Y Cf. A000040, A005062, A395827, A396152, A396153, A396155, A396156.

%K nonn,easy

%O 0,7

%A _A.H.M. Smeets_, May 20 2026