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

1,2

Comments

For more information, links, programs see A098485.

Links

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

Example

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;

Prog

See link in A098485.

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.

Sequence in context: A187850 A186965 A330386 * A174381 A184363 A331451

Adjacent sequences: A098484 A098485 A098486 * A098488 A098489 A098490

Keyword

nonn,tabl

Author

Hugo Pfoertner, Sep 15 2004

Extensions

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

Status

approved