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A230548 Twin hearts patterns packing into n X n coins. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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