

A288720


Detour index of the nhypercube graph.


1



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

0,3


COMMENTS

The longest path from a vertex to any other with the same parity will contain 2^n2 edges and the longest path from a vertex to any other with opposite parity will contain 2^n1 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(n1)  56*a(n2) + 64*a(n3).
a(n) = 2^n * (2^(2*n1)  5*2^(n2) + 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



