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%I #19 Sep 20 2017 03:37:56
%S 1,4,0,9,16,8,16,78,140,79,25,228,964,1987,1974,36,520,3920,16834,
%T 42368,62266,49,1020,11860,85275,397014,1220298,2484382,64,1806,29708,
%U 317471,2326320,12033330,44601420,119138166,81,2968,65240,962089,10087628,77784658,450193818,1979541332,6655170642
%N 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.
%C For more information, links, programs see A098485.
%H Alois P. Heinz, <a href="/A098487/b098487.txt">Rows n = 1..21, flattened</a>
%e 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:
%e X0X...X0X...X0X...X00...X00...0X0...00X...00X
%e 000...000...000...00X...000...000...X00...000
%e X00...0X0...00X...X00...X0X...X0X...00X...X0X
%e Triangle begins:
%e : 1;
%e : 4, 0;
%e : 9, 16, 8;
%e : 16, 78, 140, 79;
%e : 25, 228, 964, 1987, 1974;
%e : 36, 520, 3920, 16834, 42368, 62266;
%e : 49, 1020, 11860, 85275, 397014, 1220298, 2484382;
%e : 64, 1806, 29708, 317471, 2326320, 12033330, 44601420, 119138166;
%o See link in A098485.
%Y A098485 gives selections where all marks are connected, A090642 gives total number of possible selections.
%Y Main diagonal gives A201513.
%Y Cf. A291716, A291717, A291718, A292152, A292153, A292154, A292155, A292156.
%K nonn,tabl
%O 1,2
%A _Hugo Pfoertner_, Sep 15 2004
%E T(8,8) corrected by _Alois P. Heinz_, May 11 2017
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