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 A338709 Number of (undirected) paths in C_3 X P_n. 5
 6, 129, 1209, 8856, 57522, 348945, 2031525, 11531712, 64438638, 356590161, 1961459841, 10749416568, 58777575354, 320956083777, 1751147966157, 9549634751424, 52062358139670, 283782668909793, 1546691543230473, 8429380058864280, 45938035123043586, 250345837703068209 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..50 FORMULA 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 PROG (Python) # Using graphillion from graphillion import GraphSet def make_CnXPk(n, k):     grids = []     for i in range(1, k + 1):         for j in range(1, n):             grids.append((i + (j - 1) * k, i + j * k))         grids.append((i + (n - 1) * k, i))     for i in range(1, k * n, k):         for j in range(1, k):             grids.append((i + j - 1, i + j))     return grids def A(start, goal, n, k):     universe = make_CnXPk(n, k)     GraphSet.set_universe(universe)     paths = GraphSet.paths(start, goal)     return paths.len() def B(n, k):     m = k * n     s = 0     for i in range(1, m):         for j in range(i + 1, m + 1):             s += A(i, j, n, k)     return s def A338709(n):     return B(3, n) print([A338709(n) for n in range(1, 11)]) CROSSREFS Cf. A003689, A338960, A338961, A338962, A338963. Sequence in context: A111873 A012842 A012638 * A318528 A095695 A156475 Adjacent sequences:  A338706 A338707 A338708 * A338710 A338711 A338712 KEYWORD nonn AUTHOR Seiichi Manyama, Dec 18 2020 STATUS approved

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Last modified June 21 19:12 EDT 2021. Contains 345365 sequences. (Running on oeis4.)