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

0,4

Links

Table of n, a(n) for n=0..25.

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

Formula

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

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

Mathematica

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

Crossrefs

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

Sequence in context: A252816 A093737 A268402 * A081039 A227748 A349594

Adjacent sequences: A351526 A351527 A351528 * A351530 A351531 A351532

Keyword

nonn,easy

Author

R. J. Mathar, Feb 13 2022

Status

approved