A027683 Number of independent vertex sets of the n X n torus grid graph.

1, 7, 34, 743, 25531, 2406862, 464483559, 213256442503, 215560806324388, 498819827260367617, 2590618817013278596997, 30496896080418683388380966, 809724336154415150287031740151, 48609694845429192825410114233405807, 6589876632329358971395398453738256596574, 2018670118781080042934952855192359574137313799

Offset: 1

Author

R. H. Hardin

Keywords

• nonn
• nice
• hard

Links

• Rintaro Matsuo, Table of n, a(n) for n = 1..32
• Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, p. 73, 405.
• Eric Weisstein's World of Mathematics, Independent Vertex Set
• Eric Weisstein's World of Mathematics, Torus Grid Graph

Crossrefs

Cf. A006506 for flat version.

Cf. A067960, A201626, A212270.

Programs

Mathematica

a[n_] := With[{sets = Select[Tuples[{0, 1}, n], Count[#*RotateLeft[#], 1] == 0 &]}, Tr[MatrixPower[Table[Boole[Count[s1*s2, 1] == 0], {s1, sets}, {s2, sets}], n]]];
Table[a[n], {n, 1, 10}] (* Pjotr Buys, Jun 07 2023 *)

Extensions

Terms a(14)-a(16) from Vaclav Kotesovec, Dec 02 2011