A396156 - OEIS

%I #14 Jun 01 2026 21:35:15

%S 0,0,0,0,0,0,0,1,11,96,756,5616,40176,279936,1912896,12877051,

%T 85660331,564349986,3688427016,23944519296,154550826576,992607029856,

%U 6347453435136,40435581148441,256718608126271,1624942124231376,10257434086595256,64591283497027536,405827720428347216,2544646112736823296

%N a(n) is the number of possible outcomes having a run of 7 or more sixes when a die is rolled n times.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (11,-25,-25,-25,-25,-25,-25,-30).

%F G.f.: x^7/((6*x - 1)*(5*x^7 + 5*x^6 + 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, -25, -25, -30}, {0, 0, 0, 0, 0, 0, 0, 1}, 30] (* _Amiram Eldar_, May 26 2026 *)

%o (PARI) concat([0, 0, 0, 0, 0, 0, 0], Vec(x^7/((6*x-1)*(5*x^7+5*x^6+5*x^5+5*x^4+5*x^3+5*x^2+5*x-1)) + O(x^30)))

%Y Cf. A396158.

%Y Cf. A000040, A005062, A395827, A396152, A396153, A396154, A396155.

%K nonn,easy

%O 0,9

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