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%I #24 May 04 2021 02:12:45
%S 1,40545,750331584,11905151192865,179796299139278305,
%T 2662079368040434932480,39067130344394503972142977,
%U 570929651486775190858844600865,8326627661691818545121844900397056,121316352059447360262303173959408358625,1766658737971934774798769007686932254154689
%N Number of spanning trees in the graph P_9 x P_n.
%H Seiichi Manyama, <a href="/A334004/b334004.txt">Table of n, a(n) for n = 1..200</a>
%t a[n_] := Resultant[ChebyshevU[n - 1, x/2], ChebyshevU[8, (4 - x)/2], x]; Array[a, 11] (* _Amiram Eldar_, May 04 2021 *)
%o (PARI) {a(n) = polresultant(polchebyshev(n-1, 2, x/2), polchebyshev(8, 2, (4-x)/2))}
%o (Python)
%o # Using graphillion
%o from graphillion import GraphSet
%o import graphillion.tutorial as tl
%o def A116469(n, k):
%o if n == 1 or k == 1: return 1
%o universe = tl.grid(n - 1, k - 1)
%o GraphSet.set_universe(universe)
%o spanning_trees = GraphSet.trees(is_spanning=True)
%o return spanning_trees.len()
%o def A334004(n):
%o return A116469(n, 9)
%o print([A334004(n) for n in range(1, 10)])
%Y Row m=9 of A116469.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Apr 12 2020
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