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 A339751 Number of (undirected) paths in the 3 X n king graph. 3
 3, 235, 5148, 96956, 1622015, 25281625, 375341540, 5384233910, 75321922433, 1034169469257, 13999362291892, 187462552894846, 2489361245031701, 32843155609675341, 431132757745615932, 5637280548371484492, 73484574453020315121, 955615821857238062353, 12403944194214668554202 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..40 Eric Weisstein's World of Mathematics, Graph Path Eric Weisstein's World of Mathematics, King Graph FORMULA Empirical g.f.: x*(3 + 142*x - 1234*x^2 + 6033*x^3 - 4437*x^4 + 1913*x^5 - 647*x^6 + 24874*x^7 + 25724*x^8 + 1737*x^9 + 10969*x^10 + 22767*x^11 + 24670*x^12 + 12330*x^13 + 1616*x^14 + 240*x^15 + 1008*x^16) / ((1 - x)^2 * (-1 + 8*x + 14*x^2 + 5*x^3 + 6*x^4)^2*(1 - 13*x - 2*x^2 + 45*x^3 - 24*x^4 - 22*x^5 + 9*x^6 + 8*x^7 - 6*x^8)). - Vaclav Kotesovec, Dec 16 2020 PROG (Python) # Using graphillion from graphillion import GraphSet def make_nXk_king_graph(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)) if i < k: grids.append((i + (j - 1) * k, i + j * k + 1)) if i > 1: grids.append((i + (j - 1) * k, i + j * k - 1)) 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_nXk_king_graph(n, k) GraphSet.set_universe(universe) paths = GraphSet.paths(start, goal) return paths.len() def A307026(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 A339751(n): return A307026(n, 3) print([A339751(n) for n in range(1, 21)]) CROSSREFS Row 3 of A307026. Cf. A288527, A339761. Sequence in context: A072320 A162603 A252585 * A053970 A298277 A299370 Adjacent sequences: A339748 A339749 A339750 * A339752 A339753 A339754 KEYWORD nonn AUTHOR Seiichi Manyama, Dec 15 2020 STATUS approved

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Last modified March 30 09:39 EDT 2023. Contains 361609 sequences. (Running on oeis4.)