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 A334004 Number of spanning trees in the graph P_9 x P_n. 3

%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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Last modified September 11 15:47 EDT 2024. Contains 375836 sequences. (Running on oeis4.)