A173963 Number of nonoverlapping placements of one 1 X 1 square and one 2 X 2 square on an n X n board.
0, 0, 20, 108, 336, 800, 1620, 2940, 4928, 7776, 11700, 16940, 23760, 32448, 43316, 56700, 72960, 92480, 115668, 142956, 174800, 211680, 254100, 302588, 357696, 420000, 490100, 568620, 656208, 753536, 861300, 980220, 1111040, 1254528
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..10000
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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Magma
[(n^2 - 4) * (n-1)^2: n in [1..40]]; // Vincenzo Librandi, Sep 14 2011
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Mathematica
Table[(n^2-4)(n-1)^2,{n,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{0,0,20,108,336},40] (* Harvey P. Dale, Aug 16 2011 *)
Formula
a(n) = (n^2 - 4) * (n-1)^2.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5), with a(1)=0, a(2)=0, a(3)=20, a(4)=108, a(5)=336. - Harvey P. Dale, Aug 16 2011
G.f.: (4*x^3*((x-2)*x-5))/(x-1)^5. - Harvey P. Dale, Aug 16 2011
Comments