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 A137333 Spiral tiling numbers. 0
 3, 4, 6, 12, 36, 42, 48, 192, 294, 324, 768, 2058, 2916, 3072, 12288, 14406, 26244, 49152, 100842, 196608, 236196, 705894, 786432, 2125764, 3145728, 4941258, 12582912, 19131876, 34588806, 50331648, 172186884, 201326592, 242121642, 805306368, 1549681956 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is basically three intertwined sequences: triangular: 3*1, 3*4, 3*16, ... 3*4^n; square: 4*1, 4*9, 4*81, ... 4*9^n; hexagonal: 6*1, 6*7, 6*49, ... 6*7^n. Each number in the above sequence has a particular geometric interpretation: 3: a single triangular tile 4: a single square tile 6: a single hexagonal tile 12 = 3*4 = triangle (three sides) * 4 tiles = one triangle in the center, with 3 equally sized triangles surrounding it; 36 = 4*9 = square (four sides) * 9 tiles = one square with 8 other similar copies surrounding it; 42 = 6*7 = hexagon (six sides) * 7 tiles = one hexagon with 6 other copies surrounding it. Each number in the sequence has a prime factorization which uniquely determines whether it corresponds to a triangular, square or hexagonal tiling and the tiling's size. Factorization and rewriting into canonical form effectively becomes the inverse operation of "mixing" the three initial sequences. LINKS Table of n, a(n) for n=1..35. Paul Bourke, Spiral Honeycomb Mosaic of order 3 EXAMPLE 2058 = 6 * 7^3 = spiral honeycomb (hexagonal) mosaic of order 3, which is depicted in the linked image. MATHEMATICA With[{nn=40}, Take[Union[Flatten[Table[{3*4^Range[0, n], 4*9^Range[0, n], 6*7^Range[ 0, n]}, {n, nn}]]], nn]] (* Harvey P. Dale, Oct 20 2012 *) CROSSREFS Cf. A003401. Sequence in context: A176045 A350299 A255733 * A006719 A202855 A182857 Adjacent sequences: A137330 A137331 A137332 * A137334 A137335 A137336 KEYWORD nonn,uned AUTHOR Declan Malone (declan.malone+sloane(AT)gmail.com), Apr 20 2008 EXTENSIONS More terms from Harvey P. Dale, Oct 20 2012 STATUS approved

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Last modified June 12 18:11 EDT 2024. Contains 373359 sequences. (Running on oeis4.)