A387376 a(n) = 2 + 4^n + 2*n*(n - 1).

6, 22, 78, 282, 1066, 4158, 16470, 65650, 262290, 1048758, 4194526, 16777482, 67109178, 268435822, 1073742246, 4294967778, 17179869730, 68719477350, 274877907630, 1099511628538, 4398046511946, 17592186045342, 70368744178678, 281474976711762, 1125899906843826

Offset

1,1

Comments

For n >= 3, also the number of connected induced subgraphs in the n-double cone graph.

Links

Table of n, a(n) for n=1..25.

Eric Weisstein's World of Mathematics, Connected Graph.

Eric Weisstein's World of Mathematics, Double Cone Graph.

Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph.

Index entries for linear recurrences with constant coefficients, signature (7,-15,13,-4).

Formula

a(n) = 7*a(n-1)-15*a(n-2)+13*a(n-3)-4*a(n-4).

G.f.: -2*x*(-3+10*x-7*x^2+6*x^3)/((-1+x)^3*(-1+4*x)).

E.g.f.: exp(4*x) + 2*exp(x)*(1 + x^2) - 3. - Stefano Spezia, Aug 29 2025

Mathematica

Table[2 + 4^n + 2 n (n - 1), {n, 20}]
LinearRecurrence[{7, -15, 13, -4}, {6, 22, 78, 282}, 20]
CoefficientList[Series[-(2 (-3 + 10 x - 7 x^2 + 6 x^3)/((-1 + x)^3 (-1 + 4 x))), {x, 0, 20}], x]

Crossrefs

Sequence in context: A217530 A111566 A372239 * A200052 A051945 A253070

Adjacent sequences: A387373 A387374 A387375 * A387377 A387378 A387379

Keyword

nonn,easy

Author

Eric W. Weisstein, Aug 28 2025

Status

approved