A395827 a(n) is the number of possible outcomes having a run of 2 or more sixes when a die is rolled n times.

0, 0, 1, 11, 96, 751, 5531, 39186, 270241, 1827071, 12166176, 80043931, 521516711, 3370600266, 21637367221, 138100531451, 877053657456, 5545955929111, 34936157840291, 219337228291746, 1372926887328601, 8570680318112231, 53374194467267136, 331661324567274691

Offset

0,4

Links

Table of n, a(n) for n=0..23.

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

Formula

a(n) = A340156(6,n).

a(n) = 6^n - A180033(n).

Limit_{n -> oo} a(n+1)/a(n) = 6.

G.f.: x^2 / ((6*x - 1) * (5*x^2 + 5*x - 1)). - Amiram Eldar, May 08 2026

Mathematica

LinearRecurrence[{11, -25, -30}, {0, 0, 1}, 24] (* Amiram Eldar, May 08 2026 *)

Crossrefs

Cf. A180033, A340156.

Cf. A008466, A186244, A351529, A351530, A395828, A395829, A322053, A395830.

Sequence in context: A051446 A271632 A055286 * A396152 A396153 A396154

Adjacent sequences: A395824 A395825 A395826 * A395828 A395829 A395830

Keyword

nonn,easy

Author

A.H.M. Smeets, May 07 2026

Status

approved