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 A230550 Voids left after packing twin hearts patterns into n X n coins. 6
 1, 2, 5, 10, 13, 22, 33, 40, 51, 68, 73, 94, 113, 126, 145, 174, 181, 214, 241, 260, 287, 328, 337, 382, 417, 442, 477, 530, 541, 598, 641, 672, 715, 780, 793, 862, 913, 950, 1001, 1078, 1093, 1174, 1233, 1276, 1335, 1424 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS 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. 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. LINKS Kival Ngaokrajang, Illustration of initial terms (V) FORMULA a(n) = (n-1)^2 - 2*A230548(n). 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 PROG (Small Basic) col = 1 row = 0 For n = 2 To 100   add = 0   If Math.Remainder(n, 2) * Math.Remainder(n, 3) <> 0 Then     add = 1   EndIf   If n >= 4 And Math.Remainder(n, 2) = 0 Then     col = col + 1   EndIf   If n >= 3 And Math.Remainder(n, 3) = 0 Then     row = row + 1   EndIf   V = (n-1) * (n-1) - (col * row + add)*2   TextWindow.Write(V+", ") EndFor CROSSREFS Cf. A008795, A230370 (3-curves); A074148, A227906, A229093, A229154 (4-curves); A001399, A230267, A230276 (5-curves); A229593, A228949, A229598, A002620 (6-curves). Sequence in context: A190249 A188434 A135467 * A018571 A064233 A051952 Adjacent sequences:  A230547 A230548 A230549 * A230551 A230552 A230553 KEYWORD nonn AUTHOR Kival Ngaokrajang, Oct 23 2013 STATUS approved

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Last modified July 10 00:25 EDT 2020. Contains 335570 sequences. (Running on oeis4.)