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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
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
Sequence in context: A355761 A306948 A067241 * A120943 A087792 A192881
KEYWORD
nonn,more
AUTHOR
STATUS
approved

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