A396154 a(n) is the number of possible outcomes having a run of 5 or more sixes when a die is rolled n times.

0, 0, 0, 0, 0, 1, 11, 96, 756, 5616, 40176, 279931, 1912811, 12876066, 85650696, 564264576, 3687717456, 23938890361, 154507689791, 992285228496, 6345103937976, 40418727227856, 256599474317136, 1624110448674691, 10251689936941271, 64551976895557626, 405560928053970756

Offset

0,7

Links

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (11,-25,-25,-25,-25,-30).

Formula

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

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

Mathematica

LinearRecurrence[{11, -25, -25, -25, -25, -30}, {0, 0, 0, 0, 0, 1}, 27] (* Amiram Eldar, May 20 2026 *)

Prog

(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)))

Crossrefs

Cf. A396158.

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

Sequence in context: A395827 A396152 A396153 * A396155 A396156 A081041

Adjacent sequences: A396151 A396152 A396153 * A396155 A396156 A396157

Keyword

nonn,easy

Author

A.H.M. Smeets, May 20 2026

Status

approved