A395828 Number of septenary strings of length n that contain a specific string xx (where x is a single digit).

0, 0, 1, 13, 133, 1219, 10513, 87199, 703921, 5570263, 43409905, 334234615, 2548342369, 19272788647, 144768073297, 1081134182071, 8033636605057, 59436186232711, 438051867596209, 3217558836960727, 23562077825252065, 172076715158649895, 1253625024201023761

Offset

0,4

Links

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (13,-36,-42).

Formula

a(n) = A340156(7,n).

a(n) = 7^n - A180167(n).

G.f.: x^2 / ((7*x-1) * (6*x^2+6*x-1)). - Amiram Eldar, May 12 2026

Mathematica

LinearRecurrence[{13, -36, -42}, {0, 0, 1}, 23] (* Amiram Eldar, May 12 2026 *)

Crossrefs

Cf. A180167, A340156.

Cf. A008466, A186244, A351529, A351530, A395827, A395829, A322053, A395830.

Sequence in context: A199144 A198664 A332243 * A081042 A329019 A016153

Adjacent sequences: A395825 A395826 A395827 * A395829 A395830 A395831

Keyword

nonn,easy

Author

A.H.M. Smeets, May 12 2026

Status

approved