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 A292421 Square array T(n,k) = number of tiles crossed by the line segment (0,0) -- (n,k) in a running bond pattern tiling with square tiles, read by antidiagonals. 0
 1, 2, 2, 4, 3, 3, 4, 3, 4, 4, 5, 4, 4, 5, 5, 6, 8, 6, 7, 6, 6, 8, 7, 5, 6, 6, 7, 7, 8, 9, 6, 8, 8, 7, 8, 8, 9, 8, 12, 9, 7, 8, 10, 9, 9, 10, 10, 10, 7, 10, 10, 10, 9, 10, 10, 12, 11, 11, 8, 10, 9, 13, 10, 10, 11, 11, 12, 11, 12, 16, 12, 11, 12, 10, 12, 13, 12, 12 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Running bond pattern: the tiles form horizontal rows and for all i (row number), row i+1 is row i translated by vector (1/2, 1). The first row is supposed to contain the tile with bottom-left vertex (0,0). A tile is considered crossed if its interior intersects the line segment (0,0) -- (n,k). LINKS Table of n, a(n) for n=1..78. EXAMPLE T(3,5) = 5 because (0,0) -- (3,5) crosses the following tiles, identified by their bottom-left vertices: (0,0), (0.5,1), (1,2), (1.5,3), (2,4). T(5,3) = 6 because (0,0) -- (5,3) crosses the following tiles, identified by their bottom-left vertices: (0,0), (1,0), (1.5,1), (2.5,1), (3,2), (4,2). MATHEMATICA F[a_, b_, p_, q_, i_] := Block[{x0, x1, d}, x0 = (p/q - a/b)*i; x1 = x0 + p/q; d = Floor[x1] - Floor[x0]; If[IntegerQ[x1], d, d + 1]]; FF[a_, b_, p_, q_] := Sum[F[a, b, p, q, i], {i, 0, q - 1}]; a = 1; b = 2; Table[FF[a, b, p, s - p], {s, 2, 13}, {p, 1, s - 1}] // Flatten CROSSREFS Cf. A074712. Sequence in context: A227183 A162439 A154417 * A205563 A147594 A305425 Adjacent sequences: A292418 A292419 A292420 * A292422 A292423 A292424 KEYWORD nonn,tabl AUTHOR Luc Rousseau, Sep 16 2017 STATUS approved

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Last modified June 21 04:30 EDT 2024. Contains 373540 sequences. (Running on oeis4.)