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A339198
Number of (undirected) cycles on the n X 4 king graph.
4
85, 3459, 136597, 4847163, 171903334, 6109759868, 217211571195, 7721452793328, 274480808918598, 9757216290644264, 346848710800215246, 12329747938579785459, 438296805656767232863, 15580536695961884270466, 553855562644922140772689, 19688409342958501534182423
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 * (-336*x^16 - 360*x^15 + 187*x^14 - 4505*x^13 + 12123*x^12 + 14959*x^11 - 65728*x^10 + 50979*x^9 - 52680*x^8 + 26849*x^7 + 179877*x^6 + 22927*x^5 - 222548*x^4 + 1318*x^3 + 14878*x^2 + 399*x + 85) / ((x-1)^2 * (112*x^16 + 8*x^15 - 217*x^14 + 904*x^13 - 2866*x^12 + 1756*x^11 + 7818*x^10 - 22167*x^9 + 45698*x^8 - 61238*x^7 + 8041*x^6 + 31909*x^5 - 5819*x^4 - 538*x^3 - 36*x^2 - 34*x + 1)). - 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 A339198(n):
return A339098(n, 4)
print([A339198(n) for n in range(2, 20)])
CROSSREFS
Column 4 of A339098.
Cf. A339201.
Sequence in context: A157110 A076463 A281162 * A017801 A201799 A017748
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 27 2020
STATUS
approved