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A008855
Triangle T(n,k), n>=1, read by rows, where T(n,k) is the number of lattice polygons with area n and perimeter 2*k.
4
1, 2, 6, 1, 18, 8, 55, 2, 40, 174, 22, 168, 566, 6, 134, 676, 1868, 1, 72, 656, 2672, 6237, 30, 482, 2992, 10376, 21050, 8, 310, 2592, 13160, 39824, 71666, 2, 151, 2086, 12862, 56162, 151878, 245696, 68, 1392, 11717, 61032, 234520, 576656, 847317, 22, 864, 9332, 60864, 279492, 965136, 2181496, 2937116
OFFSET
1,2
COMMENTS
Row lengths are 1, 1, 1, 2, 2, 3, 3, 4, 5, 5, ...
LINKS
Andrey Zabolotskiy, Table of n, a(n) for n = 1..120 (rows 1..20, from Enting & Guttmann)
I. G. Enting and A. J. Guttmann, On the area of square lattice polygons, J. Statist. Phys., 58 (1990), 475-484.
EXAMPLE
T(1,2) = 1;
+--+
| |
+--+
T(2,3) = 2;
+--+
| |
+--+ +--+--+
| | | | |
+--+ +--+--+
T(3,4) = 6;
+--+
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+--+ +--+
| | | |
+--+ +--+--+--+ +--+--+
| | | | | | | | |
+--+ +--+--+--+ +--+--+
+--+ +--+--+ +--+--+
| | | | | | | |
+--+--+ +--+--+ +--+--+
| | | | | | |
+--+--+ +--+ +--+
============================================
n\k | 2 3 4 5 6 7 8 9 10
----|---------------------------------------
1 | 1;
2 | 2;
3 | 6;
4 | 1, 18;
5 | 8, 55;
6 | 2, 40, 174;
7 | 22, 168, 566;
8 | 6, 134, 676, 1868;
9 | 1, 72, 656, 2672, 6237;
CROSSREFS
KEYWORD
nonn,tabf,nice
EXTENSIONS
More terms from Sean A. Irvine, Apr 12 2018
Examples added and name edited by Seiichi Manyama, Apr 04 2020
STATUS
approved