A341704 a(n) = 20*binomial(n,6) + 2*binomial(n,3) + 1.

1, 1, 1, 3, 9, 21, 61, 211, 673, 1849, 4441, 9571, 18921, 34893, 60789, 101011, 161281, 248881, 372913, 544579, 777481, 1087941, 1495341, 2022483, 2695969, 3546601, 4609801, 5926051, 7541353, 9507709, 11883621, 14734611, 18133761, 22162273, 26910049, 32476291

Offset: 0

Author

Enrique Navarrete, Feb 17 2021

Keywords

• nonn
• easy

Comments

a(n) is the number of ternary strings of length n that contain either none or three 0's and either none or three 1's.

Examples

			a(7)=211 since the strings are the 140 permutations of 0001112, the 35 permutations of 0002222, the 35 permutations of 1112222, and 2222222.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A341703, A341705.

Formula

E.g.f.: exp(x)*(1 + x^3/6)^2.

O.g.f.:(1 - 6*x + 15*x^2 - 18*x^3 + 9*x^4 + 19*x^6)/(1 - x)^7. - Stefano Spezia, Feb 19 2021