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A230550 Voids left after packing twin hearts patterns into n X n coins.

%I A230550 #15 Dec 18 2015 18:18:44
%S A230550 1,2,5,10,13,22,33,40,51,68,73,94,113,126,145,174,181,214,241,260,287,
%T A230550 328,337,382,417,442,477,530,541,598,641,672,715,780,793,862,913,950,
%U A230550 1001,1078,1093,1174,1233,1276,1335,1424
%N A230550 Voids left after packing twin hearts patterns into n X n coins.
%C A230550 Twin hearts (6c4a type) is one of total 17 distinct patterns appearing in 3X2 coins where each pattern consists of 6 perimeter parts from each coin and forms a continuous area.
%C A230550 a(n) is the number of total voids left after packing twin hearts patterns (6c4a type: 6-curves cover 4 coins) into n X n coins with rotation not allowed. The total twin hearts patterns packing into n X n coins is A230548 and coins left is A230549. See illustration in links.
%H A230550 Kival Ngaokrajang, <a href="/A230550/a230550.pdf">Illustration of initial terms (V)</a>
%F A230550 a(n) = (n-1)^2 - 2*A230548(n).
%F A230550 G.f.: x^2 * (-2*x^10 + x^9 + 2*x^8 + 8*x^7 + 11*x^6 + 8*x^5 + 6*x^4 + 7*x^3 + 4*x^2 + 2*x + 1)/((1+x^3)*(1-x^3)^2*(1-x^2)) (conjectured). - _Ralf Stephan_, Oct 30 2013
%o A230550 (Small Basic)
%o A230550 col = 1
%o A230550 row = 0
%o A230550 For n = 2 To 100
%o A230550   add = 0
%o A230550   If Math.Remainder(n,2) * Math.Remainder(n,3) <> 0 Then
%o A230550     add = 1
%o A230550   EndIf
%o A230550   If n >= 4 And Math.Remainder(n,2) = 0 Then
%o A230550     col = col + 1
%o A230550   EndIf
%o A230550   If n >= 3 And Math.Remainder(n,3) = 0 Then
%o A230550     row = row + 1
%o A230550   EndIf
%o A230550   V = (n-1) * (n-1) - (col * row + add)*2
%o A230550   TextWindow.Write(V+", ")
%o A230550 EndFor
%Y A230550 Cf. A008795, A230370 (3-curves); A074148, A227906, A229093, A229154 (4-curves); A001399, A230267, A230276 (5-curves); A229593, A228949, A229598, A002620 (6-curves).
%K A230550 nonn
%O A230550 2,2
%A A230550 _Kival Ngaokrajang_, Oct 23 2013