|
%I #7 May 06 2019 15:52:28
%S 3,26,111,396,1235,3414,8463,19064,39555,76530,139535,241860,401427,
%T 641774,993135,1493616,2190467,3141450,4416303,6098300,8285907,
%U 11094534,14658383,19132392,24694275,31546658,39919311,50071476,62294291,76913310,94291119,114830048
%N Number of (undirected) paths in the n-dipyramidal graph.
%C Extended to a(1)-a(2) using the formula/recurrence.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DipyramidalGraph.html">Dipyramidal 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_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
%F a(n) = n*(-135 + 293*n - 180*n^2 + 80*n^3 - 15*n^4 + 2*n^5)/15.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
%F G.f.: x*(-3 - 5*x + 8*x^2 - 60*x^3 + 11*x^4 - 47*x^5)/(-1 + x)^7.
%t Table[n (-135 + 293 n - 180 n^2 + 80 n^3 - 15 n^4 + 2 n^5)/15, {n, 20}]
%t LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {3, 26, 111, 396, 1235, 3414, 8463}, 20]
%t CoefficientList[Series[(-3 - 5 x + 8 x^2 - 60 x^3 + 11 x^4 - 47 x^5)/(-1 + x)^7, {x, 0, 20}], x]
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_, May 06 2019
|
