A302390 Triameter of the n-cube-connected cycle graph.

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

Offset

3,1

Links

Table of n, a(n) for n=3..57.

Eric Weisstein's World of Mathematics, Cube-Connected Cycle Graph

Eric Weisstein's World of Mathematics, Graph Triameter

Index entries for linear recurrences with constant coefficients, signature (1, 1, -1).

Formula

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

Example

From Andrew Howroyd, Apr 16 2018: (Start)
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)

Mathematica

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 *)

Crossrefs

Sequence in context: A185126 A366959 A098956 * A014158 A171143 A058016

Adjacent sequences: A302387 A302388 A302389 * A302391 A302392 A302393

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 06 2018

Extensions

Terms a(8) and beyond from Andrew Howroyd, Apr 15 2018

Status

approved