A339117 Number of cycles in the grid graph P_5 X P_n.

10, 108, 1049, 9349, 80626, 692194, 5948291, 51139577, 439673502, 3779989098, 32497334055, 279386435639, 2401945965628, 20650054358200, 177533025653767, 1526290165248783, 13121849649571820, 112811405309454694, 969864273118112913, 8338134834111643373, 71684765011673779732

Offset: 2

Author

Seiichi Manyama, Nov 24 2020

Keywords

• nonn

Comments

a(n+1) / a(n) tends to 8.597218255461742020947886618374491114891840151635008721734194641555448999... - Vaclav Kotesovec, Nov 24 2020

Links

• Seiichi Manyama, Table of n, a(n) for n = 2..500
• 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 A339117(n):
    return A(n, 5)
print([A339117(n) for n in range(2, 15)])

Formula

Empirical g.f.: -x^2*(10 - 42*x + 149*x^2 - 300*x^3 - 393*x^4 + 693*x^5 + 230*x^6 - 473*x^7 - 72*x^8 + 202*x^9 + 84*x^10) / ((1 - x)^2 * (-1 + 13*x - 45*x^2 + 66*x^3 - 17*x^4 - 209*x^5 + 151*x^6 + 140*x^7 - 112*x^8 - 48*x^9 + 50*x^10 + 28*x^11)). - Vaclav Kotesovec, Nov 24 2020