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a(n) = 3*A000124(n-1). - R. J. Mathar, May 07 2024

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<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).

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a(n) = 3/2*(n^2 - n + 2).

3, 6, 12, 21, 33, 48, 66, 87, 111, 138, 168, 201, 237, 276, 318, 363, 411, 462, 516, 573, 633, 696, 762, 831, 903, 978, 1056, 1137, 1221, 1308, 1398, 1491, 1587, 1686, 1788, 1893, 2001, 2112, 2226, 2343, 2463, 2586, 2712, 2841, 2973, 3108, 3246, 3387, 3531, 3678

1,1

For n > 2, also the number of (non-null) connected induced subgraphs in the n-pan graph.

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PanGraph.html">Pan Graph</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Vertex-InducedSubgraph.html">Vertex-Induced Subgraph</a>

a(n) = 3/2*(n^2 - n + 2).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: -((3 x (1 - x + x^2))/(-1 + x)^3).

Table[3/2 (n^2 - n + 2), {n, 20}]

LinearRecurrence[{3, -3, 1}, {3, 6, 12}, 20]

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

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nonn,easy

Eric W. Weisstein, Aug 10 2017

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