A286513 Array read by antidiagonals: T(m,n) is the number of independent sets in the stacked prism graph C_m X P_n.
1, 1, 3, 1, 7, 4, 1, 17, 13, 7, 1, 41, 43, 35, 11, 1, 99, 142, 181, 81, 18, 1, 239, 469, 933, 621, 199, 29, 1, 577, 1549, 4811, 4741, 2309, 477, 47, 1, 1393, 5116, 24807, 36211, 26660, 8303, 1155, 76, 1, 3363, 16897, 127913, 276561, 307983, 143697, 30277, 2785, 123
Offset: 1
Examples
Table starts: ============================================================= m\n| 1 2 3 4 5 6 7 ---|--------------------------------------------------------- 1 | 1 1 1 1 1 1 1 ... 2 | 3 7 17 41 99 239 577 ... 3 | 4 13 43 142 469 1549 5116 ... 4 | 7 35 181 933 4811 24807 127913 ... 5 | 11 81 621 4741 36211 276561 2112241 ... 6 | 18 199 2309 26660 307983 3557711 41097664 ... 7 | 29 477 8303 143697 2488431 43089985 746156517 ... 8 | 47 1155 30277 788453 20546803 535404487 13951571713 ... ...
Links
- Liang Kai, Table of n, a(n) for n = 1..704 (terms up to a(435) from Andrew Howroyd)
- Kai Liang, Independent Set Enumeration and Estimation of Related Constants of Grid Graphs, arXiv:2507.04007 [math.CO], 2025. See p. 13.
- Eric Weisstein's World of Mathematics, Independent Vertex Set.
- Eric Weisstein's World of Mathematics, Stacked Prism Graph.
- Wikipedia, Independent set.
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