A098487 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.

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

Offset: 1

Author

Hugo Pfoertner, Sep 15 2004

Keywords

• nonn
• tabl

Comments

For more information, links, programs see A098485.

Examples

			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;
		

Links

• Alois P. Heinz, Rows n = 1..21, flattened

Crossrefs

A098485 gives selections where all marks are connected, A090642 gives total number of possible selections.

Main diagonal gives A201513.

Cf. A291716, A291717, A291718, A292152, A292153, A292154, A292155, A292156.

Programs

Fortran

! See link in A098485.

Extensions

T(8,8) corrected by Alois P. Heinz, May 11 2017