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A342483
a(n) = binomial(n,2)*(2^(n-2) - n).
0
0, 30, 150, 525, 1568, 4284, 11070, 27555, 66792, 158730, 371462, 858585, 1964160, 4454136, 10024254, 22410063, 49803560, 110096070, 242215974, 530573637, 1157621280, 2516574900, 5452586750, 11777596155, 25367140008, 54492385794, 116769410310, 249644959665
OFFSET
4,2
COMMENTS
a(n) is the number of ternary strings of length n with at least one 0, at least two 1's, and two 2's.
FORMULA
G.f.: x^5*(30 - 150*x + 285*x^2 - 262*x^3 + 124*x^4 - 24*x^5)/((1 - x)^4*(1 - 2*x)^3). - Stefano Spezia, Mar 14 2021
EXAMPLE
a(7)=525 since the strings are the 210 permutations of 2211000, the 210 permutations of 2211100 and the 105 permutations of 2211110.
MATHEMATICA
Array[Binomial[#, 2] (2^(# - 2) - #) &, 28, 4] (* Michael De Vlieger, Mar 13 2021 *)
LinearRecurrence[{10, -42, 96, -129, 102, -44, 8}, {0, 30, 150, 525, 1568, 4284, 11070}, 30] (* Harvey P. Dale, May 17 2024 *)
CROSSREFS
Cf. A342482.
Sequence in context: A186895 A185480 A316459 * A206040 A042760 A042762
KEYWORD
nonn,easy
AUTHOR
Enrique Navarrete, Mar 13 2021
STATUS
approved