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 A231065 Voids left after packing X patterns into an of n X n array of coins. 3
 1, 0, 5, 8, 9, 16, 17, 24, 29, 36, 41, 48, 53, 60, 65, 76, 85, 92, 101, 108, 121, 132, 141, 152, 161, 176, 189, 200, 213, 224, 241, 256, 269, 284, 297, 316, 333, 348, 365, 380, 401, 420, 437, 456, 473, 496, 517, 536, 557, 576, 601, 624, 645, 668, 689, 716, 741, 764, 789, 812, 841, 868 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS The X pattern (8c5s2 type) is a pattern in which 8 curves cover 5 coins, and is one of a total of 13 such distinct patterns that appear in a tightly-packed 3 X 3 square array of coins of identical size; each of the 8 curves is a circular arc lying along the edge of one of the 5 coins, and the 8 curves are joined end-to-end to form a continuous area. a(n) is the total number of voids (spaces among coins) left after packing X patterns into an n X n array of coins. The maximum number of X patterns that can be packed into an n X n array of coins is A231056 and coins left is A231064. a(n) is also the total number of voids left after packing "+" patterns (8c5s1 type) into an n X n array of coins. See illustration in links. LINKS Kival Ngaokrajang, Illustration of initial terms (V) FORMULA Empirical g.f.: x^2*(4*x^16 -8*x^15 +4*x^14 -4*x^13 +8*x^12 -8*x^11 +8*x^10 -4*x^9 +4*x^6 -5*x^5 +2*x^4 +2*x^3 -6*x^2 +2*x -1) / ((x -1)^3*(x^4 +x^3 +x^2 +x +1)). - Colin Barker, Nov 27 2013 PROG (Small Basic) x = 0 d1 = 1 For n = 2 To 100   If Math.Remainder(n+2, 5) = 1 Then      d2 = 0   Else     If Math.Remainder(n+2, 5) = 4 Then      d2 = -1     else      d2 = 1     EndIf   EndIf   d1[n+2] = d1[n+1] + d2   x[n+1] = x[n] + d1[n+1]   If n >= 13 And Math.Remainder(n, 5) = 3 Then     x[n] = x[n] - 1   EndIf   If n=6 or n>=16 And Math.Remainder(n, 5)=1 Then     x[n] = x[n] + 1   EndIf   V = (n-1)*(n-1) - x[n]*4   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, A230548, A230549, A230550 (6-curves). Sequence in context: A334919 A047616 A287551 * A314576 A045221 A046287 Adjacent sequences:  A231062 A231063 A231064 * A231066 A231067 A231068 KEYWORD nonn AUTHOR Kival Ngaokrajang, Nov 03 2013 STATUS approved

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Last modified July 15 00:36 EDT 2020. Contains 335762 sequences. (Running on oeis4.)