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A229598 Voids left when packing boomerangs into n X n coins.

%I A229598 #15 Dec 18 2015 18:18:42
%S A229598 1,0,3,8,5,12,21,16,27,40,33,48,65,56,75,96,85,108,133,120,147,176,
%T A229598 161,192,225,208,243,280,261,300,341,320,363,408,385,432,481,456,507,
%U A229598 560,533,588,645,616,675,736,705,768
%N A229598 Voids left when packing boomerangs into n X n coins.
%C A229598 The inverse patterns are voids or stars (consist of 4 perimeter parts of coins) appearing in n X n coins using the same rule as A229593.
%H A229598 Kival Ngaokrajang, <a href="/A229598/a229598_1.pdf">Illustration of initial terms</a>
%F A229598 Empirical g.f.: -x^2*(x+1)*(x^4-2*x^3+5*x^2-2*x+1) / ((x-1)^3*(x^2+x+1)^2). - _Colin Barker_, Oct 06 2013
%e A229598 For n = 2, there is no boomerang can be packed into 2X2 coins, there is 1 void left, a(2) = 1.
%e A229598 For n = 3, there are 2 boomerangs can be packed into 3X3 coins with no void left, a(3) = 0.
%e A229598 ...
%o A229598 (Small Basic)
%o A229598 v[2]=1
%o A229598 d[3]=-1
%o A229598 d[4]=3
%o A229598 d[5]=5
%o A229598 For n=2 To 100
%o A229598   If n+1 >=6 Then
%o A229598     If Math.Remainder(n+1,3)=0 Then
%o A229598       d[n+1]=d[n-2]-2
%o A229598     Else
%o A229598       d[n+1]=d[n-2]+4
%o A229598     EndIf
%o A229598   EndIf
%o A229598   v[n+1]=v[n]+d[n+1]
%o A229598   TextWindow.Write(v[n]+", ")
%o A229598 EndFor
%Y A229598 Cf. A229093 (Illustration of inverse clubs patterns).
%K A229598 nonn
%O A229598 2,3
%A A229598 _Kival Ngaokrajang_, Sep 26 2013