A395830 Number of hexadecimal strings of length n that contain a specific string xx (where x is a single digit).

0, 0, 1, 31, 736, 15601, 310591, 5941456, 110557921, 2015926111, 36192227776, 641841785041, 11270021820031, 196270140120496, 3394577405818561, 58366312816456351, 998470947372051616, 17005480407434466481, 288506014395807323071, 4877820327227979669136, 82217261607226450096801

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (31,-225,-240).

Formula

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

a(n) = 16^n - A395832(n).

G.f.: x^2 / ((16*x-1) * (15*x^2 + 15*x - 1)). - Amiram Eldar, May 14 2026

E.g.f.: exp(16*x) - exp(15*x/2)*(285*cosh(sqrt(285)*x/2) + 17*sqrt(285)*sinh(sqrt(285)*x/2))/285. - Stefano Spezia, May 14 2026

Mathematica

LinearRecurrence[{31, -225, -240}, {0, 0, 1}, 21] (* Amiram Eldar, May 14 2026 *)

Crossrefs

Cf. A340156, A395832.

Cf. A008466, A186244, A351529, A351530, A395827, A395828, A322053, A395829.

Sequence in context: A196988 A358179 A061252 * A096049 A166488 A051587

Adjacent sequences: A395827 A395828 A395829 * A395831 A395832 A395833

Keyword

nonn,easy

Author

A.H.M. Smeets, May 13 2026

Status

approved