cp's OEIS Frontend

A243645 Number of ways two L-tiles can be placed on an n X n square.

%I A243645 #25 Sep 26 2022 11:35:09
%S A243645 0,0,0,1,20,87,244,545,1056,1855,3032,4689,6940,9911,13740,18577,
%T A243645 24584,31935,40816,51425,63972,78679,95780,115521,138160,163967,
%U A243645 193224,226225,263276,304695,350812,401969,458520,520831,589280,664257,746164,835415,932436
%N A243645 Number of ways two L-tiles can be placed on an n X n square.
%C A243645 This sequence also represents the number of edges added to G so that it is complete, where G is a graph of (n-1)^2 nodes arranged in a rhombus and embedded in the hexagonal lattice. G begins with A045944(n-2) edges and a(n) edges are added to form a complete graph. - _John Tyler Rascoe_, Sep 24 2022
%H A243645 Alois P. Heinz, <a href="/A243645/b243645.txt">Table of n, a(n) for n = 0..1000</a>
%H A243645 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A243645 G.f.: x^3*(x^3+3*x^2-15*x-1) / (x-1)^5.
%F A243645 a(n) = (n^4-4*n^3-n^2+18*n-16)/2 for n>=2, a(n) = 0 for n<2.
%F A243645 a(n) = A083374(n-1) - A045944(n-2) for n>=2. - _John Tyler Rascoe_, Sep 24 2022
%e A243645 a(3) = 1:
%e A243645 ._____.
%e A243645 |_| |_|
%e A243645 | |___|
%e A243645 |___|_| .
%p A243645 a:= n-> `if`(n<2, 0, ((((n-4)*n-1)*n+18)*n-16)/2):
%p A243645 seq(a(n), n=0..50);
%t A243645 CoefficientList[Series[x^3 (x^3+3x^2-15x-1)/(x-1)^5,{x,0,40}],x] (* or *) LinearRecurrence[{5,-10,10,-5,1},{0,0,0,1,20,87,244},40] (* _Harvey P. Dale_, Mar 06 2016 *)
%Y A243645 Column k=2 of A243608.
%K A243645 nonn,easy
%O A243645 0,5
%A A243645 _Alois P. Heinz_, Jun 08 2014