A339119 Number of cycles in the grid graph P_7 X P_n.

21, 681, 23984, 692194, 18438929, 487150371, 12947640143, 345142437669, 9203308475041, 245355064111139, 6540331954247241, 174341025325354201, 4647322411026104632, 123881845810609904802, 3302270967098053652763, 88027348826922694314763, 2346510376337057464408514

Offset: 2

Author

Seiichi Manyama, Nov 24 2020

Keywords

• nonn

Comments

a(n+1) / a(n) tends to 26.65660630533835653493851570574867751479178653672292060740586256111131858... - Vaclav Kotesovec, Nov 24 2020

Links

• Seiichi Manyama, Table of n, a(n) for n = 2..500
• Vaclav Kotesovec, Empirical g.f.
• Eric Weisstein's World of Mathematics, Graph Cycle
• Eric Weisstein's World of Mathematics, Grid Graph

Crossrefs

Cf. A140517, A231829.

Programs

Python

# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
def A(n, k):
    universe = tl.grid(n - 1, k - 1)
    GraphSet.set_universe(universe)
    cycles = GraphSet.cycles()
    return cycles.len()
def A339119(n):
    return A(n, 7)
print([A339119(n) for n in range(2, 15)])