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 A360030 a(n) is the minimum number of equal resistors needed in an electrical network so that n nodes can be selected in this network such that there are n*(n-1)/2 distinct resistances 0 < R < oo between the selected nodes. 2
 1, 3, 5, 8, 10, 11, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 LINKS Table of n, a(n) for n=2..8. Hugo Pfoertner, Illustrated examples for the terms a(6), a(7), a(8), 17 Feb 2023. EXAMPLE a(2) = 1, [[1,2]] . 1 2 O----R1R----O R_12 = 1 . a(3) = 3, [[1,2]^2,[2,3]] . 1 .---R1R---. 2 3 O --| |-- O ---R3R--- O .---R2R---. . R_12 = 1/2, R_13 = 3/2, R_23 = 1 . a(4) = 5, node 5 hidden, [[1,2],[2,3]^2,[3,5],[4,5]] . 1 2 .---R2R---. 3 (5) 4 O ---R1R--- O --| |-- O ---R4R--- O ---R5R--- O .---R3R---. . R_12 = 1, R_13 = 3/2, R_14 = 7/2, R_23 = 1/2, R_24 = 5/2, R_34 = 2 . a(5) = 8, node 6 hidden, [[1, 2], [1, 3]^2, [2, 3], [2, 4], [3, 6], [4, 5], [4, 6]] . 1 2 4 5 O-----R1R-----O----R5R----O----R8R----O | | | | R4R R7R .---R2R---. | | | |---O----R6R----O .---R3R---. 3 (6) . R_12 = 5/9, R_13 = 7/18, R_14 = 19/18, R_15 = 37/18, R_23 = 1/2, R_24 = 13/18, R_25 = 31/18, R_34 = 8/9, R_35 = 17/9, R_45 = 1 CROSSREFS Cf. A219158, A342558, A348020. Sequence in context: A355761 A306948 A067241 * A120943 A087792 A192881 Adjacent sequences: A360027 A360028 A360029 * A360031 A360032 A360033 KEYWORD nonn,more AUTHOR Hugo Pfoertner and Rainer Rosenthal, Feb 12 2023 STATUS approved

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Last modified July 20 20:19 EDT 2024. Contains 374459 sequences. (Running on oeis4.)