A341703 a(n) = 6*binomial(n,4) + 2*binomial(n,2) + 1.

1, 1, 3, 7, 19, 51, 121, 253, 477, 829, 1351, 2091, 3103, 4447, 6189, 8401, 11161, 14553, 18667, 23599, 29451, 36331, 44353, 53637, 64309, 76501, 90351, 106003, 123607, 143319, 165301, 189721, 216753, 246577, 279379, 315351, 354691, 397603, 444297, 494989, 549901

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 two 0's and either none or two 1's.

Examples

			a(6)=121 since the strings are the 90 permutations of 110022, the 15 permutations of 002222, the 15 permutations of 112222, and 222222.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A004255, A341704, A341705.

Formula

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

From Stefano Spezia, Feb 19 2021: (Start)

O.g.f.:(1 - 4*x + 8*x^2 - 8*x^3 + 9*x^4)/(1 - x)^5.

a(n) = (4 - 10*n + 15*n^2 - 6*n^3 + n^4)/4. (End)

a(n) = 2*A004255(n-1) + 1. - Hugo Pfoertner, Feb 19 2021