login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A288719 Detour index of the n-triangular grid graph. 0
0, 6, 69, 399, 1467, 4197, 10203, 22047, 43557, 80187, 139422, 231228, 368547, 567837, 849657, 1239297, 1767453, 2470947, 3393492, 4586502, 6109947, 8033253, 10436247, 13410147, 17058597, 21498747, 26862378, 33297072, 40967427, 50056317, 60766197 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

With at least 5 vertices per side, a Hamiltonian path exists between any two vertices except in the case of a pair of vertices adjacent to a corner when the longest path will include every vertex except the corner vertex. This leads to the formula v*(v-1)^2/2-3 where v is the number of vertices. - Andrew Howroyd, Jun 19 2017

LINKS

Table of n, a(n) for n=0..30.

Eric Weisstein's World of Mathematics, Detour Index

Eric Weisstein's World of Mathematics, Triangular Grid Graph

Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

FORMULA

a(n) = (n^6 + 9*n^5 + 29*n^4 + 39*n^3 + 18*n^2 - 48)/16 for n>3. - Andrew Howroyd, Jun 19 2017

MATHEMATICA

Table[Piecewise[{{0, n == 0}, {6, n == 1}, {69, n == 2}, {399, n == 3}}, n^2 (n + 1) (n + 2) (n + 3)^2/16 - 3], {n, 0, 10}]

Table[Piecewise[{{0, n == 0}, {6, n == 1}, {69, n == 2}, {399, n == 3}}, 3 (Binomial[n + 3, 4] n (n + 3)/2 - 1)], {n, 0, 10}]

Join[{0, 6, 69, 399}, LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {3, 72, 402, 1467, 4197, 10203, 22047}, {4, 20}]]

CoefficientList[Series[-((3 x (2 + 9 x + 14 x^2 - 29 x^3 + 34 x^4 - 15 x^5 - 8 x^6 + 13 x^7 - 6 x^8 + x^9))/(-1 + x)^7), {x, 0, 20}], x]

CROSSREFS

Sequence in context: A197170 A183438 A296016 * A201535 A198699 A346938

Adjacent sequences:  A288716 A288717 A288718 * A288720 A288721 A288722

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Jun 13 2017

EXTENSIONS

a(8)-a(30) from Andrew Howroyd, Jun 19 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 19 17:19 EDT 2021. Contains 347564 sequences. (Running on oeis4.)