A351643 Number of length n word structures with all distinct runs using exactly 3 symbols.

0, 0, 1, 3, 12, 28, 81, 177, 410, 906, 1869, 4001, 8094, 16032, 32355, 62499, 120078, 227880, 436743, 805797, 1487920, 2751618, 5017143, 9063625, 16153560, 29066676, 51334289, 90784671, 157941132, 275244344, 478874505, 823848357, 1412686722, 2400778830, 4091929101

Offset: 1

Author

Andrew Howroyd, Feb 16 2022

Keywords

• nonn

Comments

Permuting the symbols will not change the structure.

Examples

			The a(3) = 1 word is 123.
The a(4) = 3 words are 1123, 1223, 1233.
The a(5) = 12 words are 11123, 11213, 11223, 11231, 11233, 12113, 12223, 12232, 12233, 12311, 12322, 12333.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Column k=3 of A351641.

Cf. A351644.

Programs

PARI

\\ See A351641 for R, S.
seq(n)={my(q=S(n), c=3); sum(k=1, c, R(q^k-1)*binomial(c, k)*(-1)^(3-k))/c!}