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A339196 Number of (undirected) cycles on the n X 2 king graph. 2
7, 30, 85, 204, 451, 954, 1969, 4008, 8095, 16278, 32653, 65412, 130939, 262002, 524137, 1048416, 2096983, 4194126, 8388421, 16777020, 33554227, 67108650, 134217505, 268435224, 536870671, 1073741574, 2147483389, 4294967028, 8589934315, 17179868898, 34359738073, 68719476432 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
LINKS
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, King Graph
FORMULA
Empirical g.f.: -x^2 * (7 + 2*x) / ((-1 + x)^2 * (-1 + 2*x)). - Vaclav Kotesovec, Dec 09 2020
PROG
(Python)
# Using graphillion
from graphillion import GraphSet
def make_nXk_king_graph(n, k):
grids = []
for i in range(1, k + 1):
for j in range(1, n):
grids.append((i + (j - 1) * k, i + j * k))
if i < k:
grids.append((i + (j - 1) * k, i + j * k + 1))
if i > 1:
grids.append((i + (j - 1) * k, i + j * k - 1))
for i in range(1, k * n, k):
for j in range(1, k):
grids.append((i + j - 1, i + j))
return grids
def A339098(n, k):
universe = make_nXk_king_graph(n, k)
GraphSet.set_universe(universe)
cycles = GraphSet.cycles()
return cycles.len()
def A339196(n):
return A339098(n, 2)
print([A339196(n) for n in range(2, 30)])
CROSSREFS
Column 2 of A339098.
Sequence in context: A083474 A030440 A256225 * A232093 A045889 A038739
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 27 2020
STATUS
approved

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Last modified May 29 18:36 EDT 2024. Contains 372952 sequences. (Running on oeis4.)