cp's OEIS Frontend

A173963 Number of nonoverlapping placements of one 1 X 1 square and one 2 X 2 square on an n X n board.

%I A173963 #25 Sep 08 2022 08:45:51
%S A173963 0,0,20,108,336,800,1620,2940,4928,7776,11700,16940,23760,32448,43316,
%T A173963 56700,72960,92480,115668,142956,174800,211680,254100,302588,357696,
%U A173963 420000,490100,568620,656208,753536,861300,980220,1111040,1254528
%N A173963 Number of nonoverlapping placements of one 1 X 1 square and one 2 X 2 square on an n X n board.
%C A173963 Also the number of placements of a horizontal and a vertical domino on the n X n board. - _Ralf Stephan_, Jun 10 2014
%H A173963 Vincenzo Librandi, <a href="/A173963/b173963.txt">Table of n, a(n) for n = 1..10000</a>
%H A173963 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A173963 a(n) = (n^2 - 4) * (n-1)^2.
%F A173963 a(n) = A000290(n-1)*A028347(n) = A085740(n-1)/4;
%F A173963 a(n) = A002378(n-2)*A028552(n-1), for n > 1.
%F A173963 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
%F A173963 G.f.: (4*x^3*((x-2)*x-5))/(x-1)^5. - _Harvey P. Dale_, Aug 16 2011
%t A173963 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 *)
%o A173963 (Magma) [(n^2 - 4) * (n-1)^2: n in [1..40]]; // _Vincenzo Librandi_, Sep 14 2011
%K A173963 nonn,easy
%O A173963 1,3
%A A173963 _Reinhard Zumkeller_, Mar 03 2010