A396156 a(n) is the number of possible outcomes having a run of 7 or more sixes when a die is rolled n times.

0, 0, 0, 0, 0, 0, 0, 1, 11, 96, 756, 5616, 40176, 279936, 1912896, 12877051, 85660331, 564349986, 3688427016, 23944519296, 154550826576, 992607029856, 6347453435136, 40435581148441, 256718608126271, 1624942124231376, 10257434086595256, 64591283497027536, 405827720428347216, 2544646112736823296

Offset

0,9

Links

Table of n, a(n) for n=0..29.

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

Formula

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)).

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

Mathematica

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

Prog

(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)))

Crossrefs

Cf. A396158.

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

Sequence in context: A396153 A396154 A396155 * A081041 A294724 A115351

Adjacent sequences: A396153 A396154 A396155 * A396157 A396158 A396159

Keyword

nonn,easy

Author

A.H.M. Smeets, May 26 2026

Status

approved