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A302390
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Triameter of the n-cube-connected cycle graph.
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0
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13, 20, 25, 32, 36, 44, 48, 56, 60, 68, 72, 80, 84, 92, 96, 104, 108, 116, 120, 128, 132, 140, 144, 152, 156, 164, 168, 176, 180, 188, 192, 200, 204, 212, 216, 224, 228, 236, 240, 248, 252, 260, 264, 272, 276, 284, 288, 296, 300, 308, 312, 320, 324, 332, 336
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OFFSET
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3,1
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LINKS
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FORMULA
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a(2n) = 12*n - 4, a(2n+1) = 12*n for n > 2. - Andrew Howroyd, Apr 15 2018
G.f.: (x^5-x^4-8*x^2+7*x+13)/(x^3-x^2-x+1). - Georg Fischer, Nov 17 2022
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EXAMPLE
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Vertices can be represented by a pair (k,w) where k in 0..n-1 is the current index and w is an n bit word.
In the following, words are shown with index zero as the rightmost bit. Example vertices are given with maximal total distance between them. Similar constructions can be used for all n. These constructions are not unique.
Case n=5: with vertices v1=(0,00000), v2=(0,01100), v3=(0,11011)
d(v1,v2)=2+5=7, d(v1,v3)=4+5=9, d(v2,v3)=4+5=9
total distance is 7 + 9 + 9 = 25 = a(5).
Case n=7: with vertices v1=(0,0000000), v2=(0,0011000), v3=(3,1111111)
d(v1,v2)=2+7=9, d(v1,v3)=7+8=15, d(v2,v3)=5+7=12
total distance is 9 + 15 + 12 = 36 = a(7).
Case n=10: with vertices v1=(0,0000000000), v2=(0,000010000), v3=(5,1111111111)
d(v1,v2)=1+10=11, d(v1,v3)=10+13=23, d(v2,v3)=9+13=22
total distance is 11 + 23 + 22 = 56 = a(10).
(End)
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MATHEMATICA
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CoefficientList[Series[(x^5-x^4-8*x^2+7*x+13)/(x^3-x^2-x+1), {x, 0, 40}], x] (* Georg Fischer, Nov 17 2022 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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