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A098487
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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 all positions are mutually isolated. Two positions (s,t),(u,v) are considered as isolated from each other if min(abs(s-u),abs(t-v))>1.
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12
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1, 4, 0, 9, 16, 8, 16, 78, 140, 79, 25, 228, 964, 1987, 1974, 36, 520, 3920, 16834, 42368, 62266, 49, 1020, 11860, 85275, 397014, 1220298, 2484382, 64, 1806, 29708, 317471, 2326320, 12033330, 44601420, 119138166, 81, 2968, 65240, 962089, 10087628, 77784658, 450193818, 1979541332, 6655170642
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OFFSET
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1,2
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COMMENTS
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For more information, links, programs see A098485.
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LINKS
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EXAMPLE
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T(3,3) = a(6) = 8 because there are the following 8 ways to pick 3 positions isolated from each other from a 3 X 3 square array:
X0X...X0X...X0X...X00...X00...0X0...00X...00X
000...000...000...00X...000...000...X00...000
X00...0X0...00X...X00...X0X...X0X...00X...X0X
Triangle begins:
: 1;
: 4, 0;
: 9, 16, 8;
: 16, 78, 140, 79;
: 25, 228, 964, 1987, 1974;
: 36, 520, 3920, 16834, 42368, 62266;
: 49, 1020, 11860, 85275, 397014, 1220298, 2484382;
: 64, 1806, 29708, 317471, 2326320, 12033330, 44601420, 119138166;
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PROG
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CROSSREFS
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A098485 gives selections where all marks are connected, A090642 gives total number of possible selections.
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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