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A024038 a(n) = 4^n - n^2. 2
1, 3, 12, 55, 240, 999, 4060, 16335, 65472, 262063, 1048476, 4194183, 16777072, 67108695, 268435260, 1073741599, 4294967040, 17179868895, 68719476412, 274877906583, 1099511627376, 4398046510663, 17592186043932 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Guo-Niu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020.
Guo-Niu Han, Enumeration of Standard Puzzles. [Cached copy]
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
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 *)
PROG
(Magma) [ 4^n-n^2: n in [0..30] ]; // Vincenzo Librandi, Dec 25 2010
(SageMath) [4^n-n^2 for n in range(31)] # G. C. Greubel, Aug 18 2023
CROSSREFS
Sequence in context: A370937 A042971 A256142 * A371429 A361356 A007199
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)