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A290768
a(n) = 3/2*(n^2 - n + 2).
1
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
OFFSET
1,1
COMMENTS
For n > 2, also the number of (non-null) connected induced subgraphs in the n-pan graph.
LINKS
Eric Weisstein's World of Mathematics, Connected Graph
Eric Weisstein's World of Mathematics, Pan Graph
Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph
FORMULA
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).
a(n) = 3*A000124(n-1). - R. J. Mathar, May 07 2024
MATHEMATICA
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]
CROSSREFS
Sequence in context: A054064 A246866 A053479 * A070333 A011779 A161809
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Aug 10 2017
STATUS
approved