A345954 a(n) is the number of ternary strings of length n with at least three 0's.

0, 0, 0, 1, 9, 51, 233, 939, 3489, 12259, 41385, 135675, 435185, 1373139, 4279161, 13210219, 40490817, 123438531, 374772041, 1134343131, 3425442705, 10326135475, 31088506905, 93507741771, 281053804769, 844319042211, 2535473709033, 7611873722299, 22847398772529, 68567563468179

Offset

0,5

Links

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (9,-30,44,-24).

Formula

a(n) = 3^n - (2^(n-3))*(n^2 + 3*n + 8).

E.g.f: exp(2x)*(exp(x)-x^2/2-x-1).

G.f.: x^3/((1 - 2*x)^3*(1 - 3*x)). - Stefano Spezia, Jul 01 2021

Example

a(5)=51 since the strings are the 10 permutations of 11000, the 10 permutations of 22000, the 20 permutations of 12000, the 5 permutations of 10000, the 5 permutations of 20000, and 00000.

Crossrefs

Cf. A001047 (at least one 0), A066810 (at least two 0's).

Sequence in context: A054549 A005746 A220236 * A061178 A246178 A213164

Adjacent sequences: A345951 A345952 A345953 * A345955 A345956 A345957

Keyword

nonn,easy

Author

Enrique Navarrete, Jun 29 2021

Status

approved