A396155 a(n) is the number of possible outcomes having a run of 6 or more sixes when a die is rolled n times.

0, 0, 0, 0, 0, 0, 1, 11, 96, 756, 5616, 40176, 279936, 1912891, 12876971, 85659426, 564341256, 3688350336, 23943886416, 154545830496, 992568888601, 6347169767231, 40433515229136, 256703819205816, 1624837770706896, 10256706688151376, 64586266099808256, 405793425954721411, 2544413573081381591

Offset

0,8

Links

Table of n, a(n) for n=0..28.

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

Formula

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)).

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

Mathematica

LinearRecurrence[{11, -25, -25, -25, -25, -25, -30}, {0, 0, 0, 0, 0, 0, 1}, 30] (* Amiram Eldar, May 26 2026 *)

Prog

(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)))

Crossrefs

Cf. A396158.

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

Sequence in context: A396152 A396153 A396154 * A396156 A081041 A294724

Adjacent sequences: A396152 A396153 A396154 * A396156 A396158 A396159

Keyword

nonn,easy

Author

A.H.M. Smeets, May 26 2026

Status

approved