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A230548 Twin hearts patterns packing into n X n coins.

%I A230548 #17 Dec 18 2015 18:18:43
%S A230548 0,1,2,3,6,7,8,12,15,16,24,25,28,35,40,41,54,55,60,70,77,78,96,97,104,
%T A230548 117,126,127,150,151,160,176,187,188,216,217,228,247,260,261,294,295,
%U A230548 308,330,345,346,384,385,400,425,442
%N A230548 Twin hearts patterns packing into n X n coins.
%C A230548 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 A230548 a(n) is the number of total twin hearts patterns (6c4a type: 6-curves cover 4 coins) packing into n X n coins with rotation not allowed. The total coins left after packing twin hearts patterns into n X n coins is A230549 and voids left is A230550. See illustration in links.
%H A230548 Kival Ngaokrajang, <a href="/A230548/a230548.pdf">Illustration of initial terms (T)</a>
%F A230548 G.f.: x^2 * (x^10 + x^8 + 2*x^5 + 3*x^4 + 2*x^3 + 2*x^2 + x)/((1+x^3) * (1-x^3)^2 * (1-x^2)) (conjectured). - _Ralf Stephan_, Oct 30 2013
%o A230548 (Small Basic)
%o A230548 col = 1
%o A230548 row = 0
%o A230548 For n = 2 To 100
%o A230548   add = 0
%o A230548   If Math.Remainder(n,2) * Math.Remainder(n,3) <> 0 Then
%o A230548     add = 1
%o A230548   EndIf
%o A230548   If n >= 4 And Math.Remainder(n,2) = 0 Then
%o A230548     col = col + 1
%o A230548   EndIf
%o A230548   If n >= 3 And Math.Remainder(n,3) = 0 Then
%o A230548     row = row + 1
%o A230548   EndIf
%o A230548   T = col * row + add
%o A230548   TextWindow.Write(T+", ")
%o A230548 EndFor
%Y A230548 Cf. A008795, A230370 (3-curves); A074148, A227906, A229093, A229154 (4-curves); A001399, A230267, A230276 (5-curves); A229593, A228949, A229598, A002620 (6-curves).
%K A230548 nonn
%O A230548 2,3
%A A230548 _Kival Ngaokrajang_, Oct 23 2013