A274047 Diameter of Generalized Petersen Graph G(n, 2).

2, 4, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 24, 25

Offset

5,1

Links

Seiichi Manyama, Table of n, a(n) for n = 5..10000

Wikipedia, Generalized Petersen Graph.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

a(n) = floor((floor(n/2)+5)/2) for n>7.

G.f.: x^5*(2 + 2*x - x^2 + x^3 - 2*x^4 - x^5 + x^6 - x^7)/((1 + x)*(1 - x)^2*(1 + x^2)). - Bruno Berselli, Jun 08 2016

a(n) = 2 + floor(n/4 + 1/2) = A002265(n+10) for n>7. - Bruno Berselli, Jun 08 2016

Mathematica

a[n_] := GraphDiameter[PetersenGraph[n, 2]]; Table[a[n], {n, 5, 30}]
LinearRecurrence[{1, 0, 0, 1, -1}, {2, 4, 3, 4, 4, 5, 5, 5}, 100] (* Harvey P. Dale, Jan 12 2020 *)

Prog

(PARI) a(n)=if(n>7, (n\2+5)\2, [4, 3, 2][n%3+1]) \\ Charles R Greathouse IV, Jun 08 2016
(Magma) [n le 7 select [4, 3, 2][n mod 3+1] else 2+Floor(n/4+1/2): n in [5..90]]; // Bruno Berselli, Jun 08 2016 - after Charles R Greathouse IV

Crossrefs

Cf. A002265.

Sequence in context: A073127 A339099 A098604 * A226644 A083172 A287797

Adjacent sequences: A274044 A274045 A274046 * A274048 A274049 A274050

Keyword

nonn,easy

Author

Nick Mayers, Jun 07 2016

Status

approved