A384506 a(n) = 2^(n-7)*(n^4 - 6*n^3 + 59*n^2 - 54*n)/3.
0, 0, 1, 6, 25, 90, 300, 952, 2912, 8640, 24960, 70400, 194304, 525824, 1397760, 3655680, 9420800, 23953408, 60162048, 149422080, 367329280, 894566400, 2159804416, 5173149696, 12299796480, 29045555200, 68157440000, 158997676032, 368880648192, 851443712000, 1955887841280
Offset: 0
Examples
a(4) = 25 since the strings are the 6 permutations of 2200, the 6 permutations of 2211, the 12 permutations of 2201, and 3333. a(6) = 300 since the strings are (number of permutations in parentheses): 220000 (15), 220001 (60), 220011 (90), 220111 (60), 221111 (15), 333300 (15), 333301 (30), and 333311 (15). Note that the 15 permutations of the string 223333 are excluded.
Links
- Index entries for linear recurrences with constant coefficients, signature (10,-40,80,-80,32).
Programs
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Mathematica
CoefficientList[Series[x^2*(1 - 4*x + 5*x^2)/(1 - 2*x)^5,{x,0,30}],x] (* or *) LinearRecurrence[{10,-40,80,-80,32},{0,0,1,6,25},31] (* James C. McMahon, Jun 04 2025 *)
Formula
E.g.f.: exp(2*x)*(x^2/2 + x^4/24).
G.f.: x^2*(1 - 4*x + 5*x^2)/(1 - 2*x)^5. - Stefano Spezia, Jun 01 2025
Comments