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A339117
Number of cycles in the grid graph P_5 X P_n.
3
10, 108, 1049, 9349, 80626, 692194, 5948291, 51139577, 439673502, 3779989098, 32497334055, 279386435639, 2401945965628, 20650054358200, 177533025653767, 1526290165248783, 13121849649571820, 112811405309454694, 969864273118112913, 8338134834111643373, 71684765011673779732
OFFSET
2,1
COMMENTS
a(n+1) / a(n) tends to 8.597218255461742020947886618374491114891840151635008721734194641555448999... - Vaclav Kotesovec, Nov 24 2020
LINKS
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Grid Graph
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
PROG
(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)])
CROSSREFS
Sequence in context: A177060 A322641 A218061 * A157084 A059524 A190957
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 24 2020
STATUS
approved