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A212798 Row 3 of array in A212796.

%I A212798 #28 Nov 22 2020 08:08:30
%S A212798 3,294,11664,367500,10609215,292626432,7839321861,205683135000,
%T A212798 5312031978672,135495143785470,3421536337406913,85686871818240000,
%U A212798 2130987634616000199,52682956706683197258,1295799745309605101520,31730077997731715070000
%N A212798 Row 3 of array in A212796.
%C A212798 A linear divisibility sequence of order 10. - _Peter Bala_, May 04 2014
%H A212798 Seiichi Manyama, <a href="/A212798/b212798.txt">Table of n, a(n) for n = 1..200</a>
%H A212798 Germain Kreweras, <a href="http://dx.doi.org/10.1016/0095-8956(78)90021-7">Complexite et circuits Euleriens dans les sommes tensorielles de graphes</a>, J. Combin. Theory, B 24 (1978), 202-212. See p. 210, Parag. 4.
%H A212798 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%H A212798 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (58,-1131,8700,-29493,43734,-29493,8700,-1131,58,-1).
%F A212798 From _Peter Bala_, May 04 2014: (Start)
%F A212798 a(n) = n/3*(-2 + ( (5 + sqrt(21))/2 )^n + ( (5 - sqrt(21))/2 )^n)^2 = 3*n*A054493(n-1)^2.
%F A212798 O.g.f.: 3*(x^8 + 40*x^7 - 665*x^6 - 866*x^5 + 5626*x^4 - 866*x^3 - 665*x^2 + 40*x + 1)/( (x - 1)^2*(x^2 - 5*x + 1)^2*(x^2 - 23*x + 1)^2 ). (End)
%p A212798 seq(simplify(n/3*(-2 + ( (5 + sqrt(21))/2 )^n + ( (5 - sqrt(21))/2 )^n)^2), n = 1..14); # _Peter Bala_, May 04 2014
%o A212798 (Python)
%o A212798 # Using graphillion
%o A212798 from graphillion import GraphSet
%o A212798 def make_CnXCk(n, k):
%o A212798     grids = []
%o A212798     for i in range(1, k + 1):
%o A212798         for j in range(1, n):
%o A212798             grids.append((i + (j - 1) * k, i + j * k))
%o A212798         grids.append((i + (n - 1) * k, i))
%o A212798     for i in range(1, k * n, k):
%o A212798         for j in range(1, k):
%o A212798             grids.append((i + j - 1, i + j))
%o A212798         grids.append((i + k - 1, i))
%o A212798     return grids
%o A212798 def A212798(n):
%o A212798     if n == 1: return 3
%o A212798     if n == 2: return 294
%o A212798     universe = make_CnXCk(n, 3)
%o A212798     GraphSet.set_universe(universe)
%o A212798     spanning_trees = GraphSet.trees(is_spanning=True)
%o A212798     return spanning_trees.len()
%o A212798 print([A212798(n) for n in range(1, 30)])  # _Seiichi Manyama_, Nov 22 2020
%Y A212798 Cf. A212796, A054493.
%K A212798 nonn,easy
%O A212798 1,1
%A A212798 _N. J. A. Sloane_, May 27 2012
%E A212798 More terms from _Peter Bala_, May 04 2014