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A334004
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Number of spanning trees in the graph P_9 x P_n.
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3
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1, 40545, 750331584, 11905151192865, 179796299139278305, 2662079368040434932480, 39067130344394503972142977, 570929651486775190858844600865, 8326627661691818545121844900397056, 121316352059447360262303173959408358625, 1766658737971934774798769007686932254154689
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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MATHEMATICA
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a[n_] := Resultant[ChebyshevU[n - 1, x/2], ChebyshevU[8, (4 - x)/2], x]; Array[a, 11] (* Amiram Eldar, May 04 2021 *)
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PROG
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(PARI) {a(n) = polresultant(polchebyshev(n-1, 2, x/2), polchebyshev(8, 2, (4-x)/2))}
(Python)
# Using graphillion
from graphillion import GraphSet
import graphillion.tutorial as tl
if n == 1 or k == 1: return 1
universe = tl.grid(n - 1, k - 1)
GraphSet.set_universe(universe)
spanning_trees = GraphSet.trees(is_spanning=True)
return spanning_trees.len()
print([A334004(n) for n in range(1, 10)])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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