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Longest path length in the n X n fiveleaper graph.

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`%I #10 Jun 14 2019 23:11:35
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`%S 0,0,0,0,2,19,47,63,80,99,120,143,168,195,224,255,288,323,360,399,440,
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`%T 483,528,575,624,675,728,783,840
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`%N Longest path length in the n X n fiveleaper graph.
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`%C The n X n fiveleaper graph is connected for n >=8 and traceable from n = 8 up to at least n = 29, meaning a(n) = n^2 - 1 for a(n) with 8 <= n <= 29 (and probably all larger n).
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`%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FiveleaperGraph.html">Fiveleaper Graph</a>
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`%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LongestPath.html">Longest Path</a>
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`%F Conjectures from _Colin Barker_, Jun 14 2019: (Start)
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`%F G.f.: x^5*(2 + 13*x - 4*x^2 - 23*x^3 + 13*x^4 + x^5) / (1 - x)^3.
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`%F a(n) = n^2 - 1 for n>7.
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`%F (End)
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`%Y Cf. A307553 (number of longest paths).
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`%K nonn,more
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`%O 1,5
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`%A _Eric W. Weisstein_, Apr 14 2019
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