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 A339196 Number of (undirected) cycles on the n X 2 king graph. 2
 7, 30, 85, 204, 451, 954, 1969, 4008, 8095, 16278, 32653, 65412, 130939, 262002, 524137, 1048416, 2096983, 4194126, 8388421, 16777020, 33554227, 67108650, 134217505, 268435224, 536870671, 1073741574, 2147483389, 4294967028, 8589934315, 17179868898, 34359738073, 68719476432 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 LINKS Seiichi Manyama, Table of n, a(n) for n = 2..1000 Eric Weisstein's World of Mathematics, Graph Cycle Eric Weisstein's World of Mathematics, King Graph FORMULA Empirical g.f.: -x^2 * (7 + 2*x) / ((-1 + x)^2 * (-1 + 2*x)). - Vaclav Kotesovec, Dec 09 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 A339098(n, k): universe = make_nXk_king_graph(n, k) GraphSet.set_universe(universe) cycles = GraphSet.cycles() return cycles.len() def A339196(n): return A339098(n, 2) print([A339196(n) for n in range(2, 30)]) CROSSREFS Column 2 of A339098. Sequence in context: A083474 A030440 A256225 * A232093 A045889 A038739 Adjacent sequences: A339193 A339194 A339195 * A339197 A339198 A339199 KEYWORD nonn AUTHOR Seiichi Manyama, Nov 27 2020 STATUS approved

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Last modified May 29 18:36 EDT 2024. Contains 372952 sequences. (Running on oeis4.)