A288720 Detour index of the n-hypercube graph.

0, 1, 16, 184, 1744, 15136, 126016, 1028224, 8306944, 66781696, 535561216, 4289726464, 34338770944, 274794029056, 2198687727616, 17590843899904, 140732119711744, 1125878432137216, 9007113355657216, 72057250441068544, 576459377914937344

Offset

0,3

Comments

The longest path from a vertex to any other with the same parity will contain 2^n-2 edges and the longest path from a vertex to any other with opposite parity will contain 2^n-1 edges. This leads to a simple formula for the detour index. - Andrew Howroyd, Jun 19 2017

Links

Table of n, a(n) for n=0..20.

Eric Weisstein's World of Mathematics, Detour Index

Eric Weisstein's World of Mathematics, Hypercube Graph

Index entries for linear recurrences with constant coefficients, signature (14,-56,64).

Formula

G.f.: x*(1 + 2*x + 16*x^2)/((1 - 2*x)*(1 - 4*x)*(1 - 8*x)). [Amended by Bruno Berselli, Apr 03 2019]

a(n) = 14*a(n-1) - 56*a(n-2) + 64*a(n-3).

a(n) = 2^n * (2^(2*n-1) - 5*2^(n-2) + 1) for n > 0. - Andrew Howroyd, Jun 19 2017

a(n) = A296819(2^n). - Andrew Howroyd, Dec 23 2017

Mathematica

LinearRecurrence[{14, -56, 64}, {0, 1, 16, 184}, 21] (* a(0)=0 amended by Georg Fischer, Apr 03 2019 *)

Crossrefs

Cf. A296778, A296819.

Sequence in context: A231135 A230992 A016298 * A125428 A203391 A016249

Adjacent sequences: A288717 A288718 A288719 * A288721 A288722 A288723

Keyword

nonn,easy

Author

Eric W. Weisstein, Jun 13 2017

Extensions

a(6)-a(20) from Andrew Howroyd, Jun 19 2017

Status

approved