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A341703
a(n) = 6*binomial(n,4) + 2*binomial(n,2) + 1.
2
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
0,3
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.
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
EXAMPLE
a(6)=121 since the strings are the 90 permutations of 110022, the 15 permutations of 002222, the 15 permutations of 112222, and 222222.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Enrique Navarrete, Feb 17 2021
STATUS
approved