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Number of (undirected) paths in the n-book graph.
0

%I #5 May 06 2019 15:53:07

%S 12,49,136,297,556,937,1464,2161,3052,4161,5512,7129,9036,11257,13816,

%T 16737,20044,23761,27912,32521,37612,43209,49336,56017,63276,71137,

%U 79624,88761,98572,109081,120312,132289,145036,158577,172936,188137,204204,221161,239032

%N Number of (undirected) paths in the n-book graph.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BookGraph.html">Book Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphPath.html">Graph Path</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1).

%F a(n) = 4*n^3 + n^2 + 6*n + 1.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

%F G.f.: x*(12 + x + 12*x^2 - x^3)/(-1 + x)^4.

%t Table[4 n^3 + n^2 + 6 n + 1, {n, 20}]

%t LinearRecurrence[{4, -6, 4, -1}, {12, 49, 136, 297}, 20]

%t CoefficientList[Series[(12 + x + 12 x^2 - x^3)/(-1 + x)^4, {x, 0, 20}], x]

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, May 06 2019