A243645 - OEIS

%I #25 Sep 26 2022 11:35:09

%S 0,0,0,1,20,87,244,545,1056,1855,3032,4689,6940,9911,13740,18577,

%T 24584,31935,40816,51425,63972,78679,95780,115521,138160,163967,

%U 193224,226225,263276,304695,350812,401969,458520,520831,589280,664257,746164,835415,932436

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

%C 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 Alois P. Heinz, <a href="/A243645/b243645.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F G.f.: x^3*(x^3+3*x^2-15*x-1) / (x-1)^5.

%F a(n) = (n^4-4*n^3-n^2+18*n-16)/2 for n>=2, a(n) = 0 for n<2.

%F a(n) = A083374(n-1) - A045944(n-2) for n>=2. - _John Tyler Rascoe_, Sep 24 2022

%e a(3) = 1:

%e ._____.

%e |_| |_|

%e | |___|

%e |___|_| .

%p a:= n-> `if`(n<2, 0, ((((n-4)*n-1)*n+18)*n-16)/2):

%p seq(a(n), n=0..50);

%t 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 Column k=2 of A243608.

%K nonn,easy

%O 0,5

%A _Alois P. Heinz_, Jun 08 2014