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%I #26 Dec 19 2020 11:45:13
%S 6,129,1209,8856,57522,348945,2031525,11531712,64438638,356590161,
%T 1961459841,10749416568,58777575354,320956083777,1751147966157,
%U 9549634751424,52062358139670,283782668909793,1546691543230473,8429380058864280,45938035123043586,250345837703068209
%N Number of (undirected) paths in C_3 X P_n.
%H Seiichi Manyama, <a href="/A338709/b338709.txt">Table of n, a(n) for n = 1..50</a>
%F Empirical g.f.: 3*x*(2 + 15*x - 53*x^2 + 89*x^3 - 37*x^4) / ((1 - x)^2 * (1 - 3*x)^2 * (1 - 6*x + 3*x^2)). - _Vaclav Kotesovec_, Dec 19 2020
%o (Python)
%o # Using graphillion
%o from graphillion import GraphSet
%o def make_CnXPk(n, k):
%o grids = []
%o for i in range(1, k + 1):
%o for j in range(1, n):
%o grids.append((i + (j - 1) * k, i + j * k))
%o grids.append((i + (n - 1) * k, i))
%o for i in range(1, k * n, k):
%o for j in range(1, k):
%o grids.append((i + j - 1, i + j))
%o return grids
%o def A(start, goal, n, k):
%o universe = make_CnXPk(n, k)
%o GraphSet.set_universe(universe)
%o paths = GraphSet.paths(start, goal)
%o return paths.len()
%o def B(n, k):
%o m = k * n
%o s = 0
%o for i in range(1, m):
%o for j in range(i + 1, m + 1):
%o s += A(i, j, n, k)
%o return s
%o def A338709(n):
%o return B(3, n)
%o print([A338709(n) for n in range(1, 11)])
%Y Cf. A003689, A338960, A338961, A338962, A338963.
%K nonn
%O 1,1
%A _Seiichi Manyama_, Dec 18 2020
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