A048493 a(n) = (n+1)*2^n - n.

1, 3, 10, 29, 76, 187, 442, 1017, 2296, 5111, 11254, 24565, 53236, 114675, 245746, 524273, 1114096, 2359279, 4980718, 10485741, 22020076, 46137323, 96468970, 201326569, 419430376, 872415207, 1811939302, 3758096357, 7784628196, 16106127331, 33285996514

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

Old definition was: "a(n) = T(n,n), array T given by A048483".

Also the number of connected induced subgraphs in the n-sunlet graph. - Eric W. Weisstein, May 25 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000
• Eric Weisstein's World of Mathematics, Sunlet Graph
• Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph
• Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).

Crossrefs

Cf. A058877.

Programs

Magma

[(n+1)*2^n-n: n in [0..30]]; // Vincenzo Librandi, Sep 26 2011

Mathematica

Table[(n + 1) 2^n - n, {n, 20}] (* Eric W. Weisstein, May 25 2017 *)
Table[2^n + (2^n - 1) n, {n, 20}] (* Eric W. Weisstein, May 25 2017 *)
LinearRecurrence[{6, -13, 12, -4}, {3, 10, 29, 76}, 20] (* Eric W. Weisstein, May 25 2017 *)

PARI

Vec(-(4*x^3-5*x^2+3*x-1)/((x-1)^2*(2*x-1)^2) + O(x^100)) \\ Colin Barker, Nov 26 2014

Formula

a(n) = (n+1)*2^n-n. - Vladeta Jovovic, Feb 28 2003

a(n) = 5*a(n-1)-7*a(n-2)-a(n-3)+8*a(n-4)-4*a(n-5). - Colin Barker, Nov 26 2014

G.f.: -(4*x^3-5*x^2+3*x-1) / ((x-1)^2*(2*x-1)^2). - Colin Barker, Nov 26 2014

Extensions

Description changed to more explicit formula by Eric W. Weisstein, May 25 2017