A351529 The number of quaternary strings of length n containing 00.

0, 0, 1, 7, 40, 205, 991, 4612, 20905, 92935, 407056, 1762117, 7556095, 32148940, 135892321, 571232647, 2389810360, 9956870845, 41335010911, 171055514452, 705891052825, 2905717608775, 11934337612576, 48918212175157, 200149835407615, 817572886925980

Offset: 0

Author

R. J. Mathar, Feb 13 2022

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-9,-12).

Crossrefs

Cf. A008466 (2-ary), A186244 (3-ary), A351530 (5-ary), A125145 (not containing 00).

Programs

Mathematica

LinearRecurrence[{7,-9,-12},{0,0,1},30] (* Harvey P. Dale, Feb 27 2023 *)

Formula

G.f.: x^2 / ( (4*x-1)*(3*x^2+3*x-1) ).

a(n) = 4^n - A125145(n).