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A098485
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Triangle T(m,k) read by rows, where T(m,k) is the number of ways in which 1 <= k <= m positions can be picked in an m X m square array such that their adjacency graph consists of a single component. Two positions (s,t), (u,v) are considered as adjacent if max(abs(s-u), abs(t-v)) <= 1.
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10
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1, 4, 6, 9, 20, 48, 16, 42, 132, 419, 25, 72, 256, 973, 3682, 36, 110, 420, 1747, 7484, 31992, 49, 156, 624, 2741, 12562, 58620, 273556, 64, 210, 868, 3955, 18916, 92912, 462104, 2927505, 81, 272, 1152, 5389, 26546, 134868, 697836, 3644935, 19082018
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OFFSET
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1,2
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COMMENTS
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Number of ways to mark the numbers on a square board on a lottery play slip such that one connected graphic pattern is formed. For the lottery "mark 6 numbers of 49 on a 7 X 7 grid of numbers" that is played in many countries, there are T(7,6)=58620 (out of binomial(49,6)=13983816) different combinations of 6 numbers whose graphic pattern on the board forms one connected component.
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LINKS
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EXAMPLE
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a(5)=T(3,2)=20 because there are 20 ways to mark two positions in a 3 X 3 square grid such that the two picked positions are either row-wise, column-wise or diagonally adjacent:
XX0...X00...X00...0XX...0X0...0X0...0X0...00X...00X...000
000...X00...0X0...000...X00...0X0...00X...0X0...00X...XX0
000...000...000...000...000...000...000...000...000...000
.........................................................
000...000...000...000...000...000...000...000...000...000
000...X00...0X0...000...X00...0X0...00X...0X0...00X...0XX
XX0...X00...X00...0XX...0X0...0X0...0X0...00X...00X...000
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PROG
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(Fortran) c See link.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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