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 A227906 Coins left after packing heart patterns (fixed orientation) into n X n coins. 7
 2, 4, 4, 9, 6, 13, 8, 17, 10, 21, 12, 25, 14, 29, 16, 33, 18, 37, 20, 41, 22, 45, 24, 49, 26, 53, 28, 57, 30, 61, 32, 65, 34, 69, 36, 73, 38, 77, 40, 81, 42, 85, 44, 89, 46, 93, 48, 97, 50, 101, 52, 105, 54, 109, 56, 113, 58, 117, 60, 121 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS From a Japanese movie, the girl told her boyfriend that she saw a heart in 4 coins. Actually there are total 6 distinct patterns appearing in 2X2 coins which each pattern consist of a part of circumference of each coin and forms a continuous area. a(n) is the number of coins left after packing fixed orientation heart patterns (type 4c2s1: 4-curve cover 2 coins and symmetry) into n X n coins. The total heart number is A093005 and voids left is A093353. See illustration in links. LINKS Kival Ngaokrajang, Illustration of initial terms (U) Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1). FORMULA From Colin Barker, Oct 30 2013: (Start) a(n) = (-1+(-1)^n-(-3+(-1)^n)*n)/2 for n>3. a(n) = n for n>3 and even. a(n) = 2*n-1 for n>3 and odd. a(n) = 2*a(n-2)-a(n-4) for n>7. G.f.: -x^2*(x^5-x^3-4*x-2) / ((x-1)^2*(x+1)^2).(End) MATHEMATICA With[{nn=60}, Join[{2, 4}, Riffle[Range[4, nn, 2], Range[9, 2nn+1, 4]]]] (* Harvey P. Dale, Feb 11 2015 *) PROG (Small Basic) For n = 2 To 100   If Math.Remainder(n, 2) = 0 then     a = n   Else     a = a + n     If n = 3 then       a = a - 1     endif   EndIf   TextWindow.Write(a+", ") EndFor (PARI) Vec(-x^2*(x^5-x^3-4*x-2)/((x-1)^2*(x+1)^2) + O(x^100)) \\ Colin Barker, Oct 30 2013 CROSSREFS Cf. A008795, A230370 (3-curves), A074148, A229093, A229154 (4-curves), A001399, A230267, A230276 (5-curves), A229593, A228949, A229598 (6-curves). Sequence in context: A010464 A187209 A006579 * A195727 A256701 A292381 Adjacent sequences:  A227903 A227904 A227905 * A227907 A227908 A227909 KEYWORD nonn,easy AUTHOR Kival Ngaokrajang, Oct 19 2013 STATUS approved

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