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
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 13 2017
EXTENSIONS
a(6)-a(20) from Andrew Howroyd, Jun 19 2017
STATUS
approved