A005367 a(n) = 2*(2^n + 1)*(2^(n+1) - 1).

4, 18, 70, 270, 1054, 4158, 16510, 65790, 262654, 1049598, 4196350, 16781310, 67117054, 268451838, 1073774590, 4295032830, 17180000254, 68719738878, 274878431230, 1099512676350, 4398048608254, 17592190238718, 70368752566270, 281474993487870, 1125899940397054

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Crossrefs

Cf. A092431.

Programs

Magma

[2*(2^n + 1)*(2^(n + 1) - 1): n in [0..50]]; // G. C. Greubel, Oct 21 2017

Mathematica

Table[2*(2^n + 1)*(2^(n + 1) - 1), {n, 0, 50}] (* G. C. Greubel, Oct 21 2017 *)

PARI

for(n=0,50, print1(2*(2^n + 1)*(2^(n + 1) - 1), ", ")) \\ G. C. Greubel, Oct 21 2017

Formula

G.f.: 2*(2 - 5*x)/((1 - x)*(1 - 2*x)*(1 - 4*x)). - Ilya Gutkovskiy, Feb 24 2017

From G. C. Greubel, Oct 21 2017: (Start)

E.g.f.: 2*exp(x)*(2*exp(3*x) + exp(x) - 1).

a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3). (End)

a(n) = 2 * A092431(n+1). - Alois P. Heinz, Feb 02 2024

a(n) = 4^(n+1) + 2^(n+1) - 2. - Ramzan Guekhaev, Feb 02 2024

Extensions

An incorrect g.f. was deleted by N. J. A. Sloane, Sep 20 2008