A395832 Number of hexadecimal strings of length n that do not contain a specific string xx (where x is a single digit).

1, 16, 255, 4065, 64800, 1032975, 16466625, 262494000, 4184409375, 66703550625, 1063319400000, 16950344259375, 270204954890625, 4307329487250000, 68663016632109375, 1094555191790390625, 17448273126337500000, 278142424771918359375, 4433860468473837890625, 70680043398686343750000

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (15,15).

Formula

a(n) = 16^n - A340156(16,n).

a(n) = 16^n - A395830(n).

G.f.: -(x + 1)/(15*x^2 + 15*x - 1). - Amiram Eldar, May 16 2026

Mathematica

LinearRecurrence[{15, 15}, {1, 16}, 20] (* Amiram Eldar, May 16 2026 *)

Prog

(PARI) Vec(-(x + 1)/(15*x^2 + 15*x - 1) + O(x^20))

Crossrefs

Cf. A340156, A395830.

Cf. A000045, A028859, A125145, A086347, A180033, A180167, A395831, A322054.

Sequence in context: A370964 A171321 A077412 * A208498 A207586 A208071

Adjacent sequences: A395829 A395830 A395831 * A395833 A395834 A395835

Keyword

nonn,easy

Author

A.H.M. Smeets, May 16 2026

Status

approved