A003222 a(n) = 2^(3*n+1) - 2*n*(2*n+1).

2, 10, 108, 982, 8120, 65426, 524132, 4194094, 33554160, 268435114, 2147483228, 17179868678, 137438952872, 1099511627074, 8796093021396, 70368744176734, 562949953420256, 4503599627369306, 36028797018962636, 288230376151710262, 2305843009213692312, 18446744073709549810

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (11,-27,25,-8).

Crossrefs

Cf. A002943, A013730.

Programs

Magma

[2^(3*n+1)-2*n*(2*n+1): n in [0..20]]; // Vincenzo Librandi, Jun 26 2011

PARI

a(n) = 2^(3*n+1)-2*n*(2*n+1); \\ Altug Alkan, Sep 21 2018

Formula

a(n) = A013730(n) - A002943(n).

From R. J. Mathar, May 05 2010: (Start)

a(n) = 11*a(n-1) - 27*a(n-2) + 25*a(n-3) - 8*a(n-4).

G.f.: 2*(1 - 6*x + 26*x^2 + 7*x^3)/((8*x-1)*(x-1)^3). (End)

E.g.f.: 2*exp(x)*(exp(7*x) - x*(3 + 2*x)). - Elmo R. Oliveira, Mar 06 2025