A308579 a(n) = (9*2^n - 6*n - 10)/2.

1, 7, 22, 55, 124, 265, 550, 1123, 2272, 4573, 9178, 18391, 36820, 73681, 147406, 294859, 589768, 1179589, 2359234, 4718527, 9437116, 18874297, 37748662, 75497395, 150994864, 301989805, 603979690, 1207959463, 2415919012, 4831838113, 9663676318, 19327352731

Offset

1,2

Comments

Number of connected induced subgraphs in the (2*n-1)-triangular snake graph.

Links

Table of n, a(n) for n=1..32.

Eric Weisstein's World of Mathematics, Connected Graph

Eric Weisstein's World of Mathematics, Triangular Snake Graph

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

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Formula

a(n) = (9*2^n - 6*n - 10)/2.

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3).

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

E.g.f.: exp(x)*(5*cosh(x) + 4*sinh(x) - 3*x - 5). - Stefano Spezia, May 31 2023

Mathematica

Table[(9 2^n - 6 n - 10)/2, {n, 20}]
LinearRecurrence[{4, -5, 2}, {1, 7, 22}, 20]
CoefficientList[Series[(-1 - 3 x + x^2)/((-1 + x)^2 (-1 + 2 x)), {x, 0, 20}], x]

Crossrefs

Sequence in context: A188377 A374973 A213585 * A246831 A354430 A122238

Adjacent sequences: A308576 A308577 A308578 * A308580 A308581 A308582

Keyword

nonn,easy

Author

Eric W. Weisstein, Jun 08 2019

Status

approved