A308580 a(n) = 3*2^n + n^2 - n.

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

Table of n, a(n) for n=0..33.

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

Index entries for linear recurrences with constant coefficients, signature (5, -9, 7, -2).

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

Adjacent sequences: A308577 A308578 A308579 * A308581 A308582 A308583

Keyword

nonn,easy

Author

Eric W. Weisstein, Jun 08 2019

Status

approved