STATUS
proposed
approved
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Revision History for A098487
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
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.
(history; published version)
(history; published version)
STATUS
editing
proposed
NAME
Lower triangle 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.
STATUS
approved
editing
STATUS
editing
approved
LINKS
Alois P. Heinz, <a href="/A098487/b098487.txt">Table of n, a(n) for Rows n = 1..23121, flattened</a>
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:
: 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, <a href="/A098487/b098487.txt">Table of n, a(n) for n = 1..231</a>
CROSSREFS
Main diagonal gives A201513.
EXTENSIONS
T(8,8) corrected by Alois P. Heinz, May 11 2017
DATA
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, 177418469, 119138166, 81, 2968, 65240, 962089, 10087628, 77784658, 450193818, 1979541332, 6655170642
EXAMPLE
64, 1806, 29708, 317471, 2326320, 12033330, 44601420, 177418469119138166;
STATUS
approved
editing
STATUS
reviewed
approved