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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 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
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
Sequence in context: A182895 A087224 A308398 * A078059 A018031 A052948
KEYWORD
nonn,easy
AUTHOR
Enrique Navarrete, Feb 17 2021
STATUS
approved

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Last modified March 28 15:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)