A230548 Twin hearts patterns packing into n X n coins.

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, 117, 126, 127, 150, 151, 160, 176, 187, 188, 216, 217, 228, 247, 260, 261, 294, 295, 308, 330, 345, 346, 384, 385, 400, 425, 442

Offset

2,3

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 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.

Links

Table of n, a(n) for n=2..52.

Kival Ngaokrajang, Illustration of initial terms (T)

Formula

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

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
  T = col * row + add
  TextWindow.Write(T+", ")
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: A138683 A072426 A189137 * A294375 A166458 A189013

Adjacent sequences: A230545 A230546 A230547 * A230549 A230550 A230551

Keyword

nonn

Author

Kival Ngaokrajang, Oct 23 2013

Status

approved