A024038 a(n) = 4^n - n^2.

1, 3, 12, 55, 240, 999, 4060, 16335, 65472, 262063, 1048476, 4194183, 16777072, 67108695, 268435260, 1073741599, 4294967040, 17179868895, 68719476412, 274877906583, 1099511627376, 4398046510663, 17592186043932

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Guo-Niu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020.
• Guo-Niu Han, Enumeration of Standard Puzzles. [Cached copy]
• Index entries for linear recurrences with constant coefficients, signature (7,-15,13,-4).

Crossrefs

Cf. A000290, A000302, A000325, A006127.

Programs

Magma

[ 4^n-n^2: n in [0..30] ]; // Vincenzo Librandi, Dec 25 2010

Mathematica

Table[4^n-n^2,{n,0,30}] (* or *) LinearRecurrence[{7,-15,13,-4},{1,3,12,55},30] (* Harvey P. Dale, Sep 14 2013 *)

SageMath

[4^n-n^2 for n in range(31)] # G. C. Greubel, Aug 18 2023

Formula

a(n) = A000325(n)*A006127(n). - Reinhard Zumkeller, Apr 10 2010

G.f.: (1 - 4*x + 6*x^2 + 3*x^3)/((1 - x)^3*(1 - 4*x)). - Colin Barker, May 29 2012

E.g.f.: exp(4*x) - x*(1 + x)*exp(x). - G. C. Greubel, Aug 18 2023