login
A308580
a(n) = 3*2^n + n^2 - n.
1
3, 6, 14, 30, 60, 116, 222, 426, 824, 1608, 3162, 6254, 12420, 24732, 49334, 98514, 196848, 393488, 786738, 1573206, 3146108, 6291876, 12583374, 25166330, 50332200, 100663896, 201327242, 402653886, 805307124, 1610613548, 3221226342, 6442451874, 12884902880, 25769804832
OFFSET
0,1
COMMENTS
Number of connected induced subgraphs in the n-dipyramidal graph (for n >=3).
LINKS
Eric Weisstein's World of Mathematics, Connected Graph
Eric Weisstein's World of Mathematics, Dipyramidal Graph
Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph
FORMULA
a(n) = 3*2^n + n^2 - n.
a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4).
G.f.: (3 - 9*x + 11*x^2 - 7*x^3)/((-1 + x)^3*(-1 + 2*x)).
MATHEMATICA
Table[3 2^n + n^2 - n, {n, 0, 40}]
LinearRecurrence[{5, -9, 7, -2}, {6, 14, 30, 60}, {0, 20}]
CoefficientList[Series[(3 - 9 x + 11 x^2 - 7 x^3)/((-1 + x)^3 (-1 + 2 x)), {x, 0, 20}], x]
CROSSREFS
Sequence in context: A307457 A077067 A083797 * A192672 A175656 A196450
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 08 2019
STATUS
approved