OFFSET
0,1
COMMENTS
Answer to the problem A1 proposed during the 51th Putnam Competition in 1990 (see Kedlaya and Larson links). - Bernard Schott, Mar 29 2023
REFERENCES
Ron Larson, Robert P. Hostetler and Bruce H. Edwards, Exercise 135 in Calculus of a Single Variable for Advanced High School Students, Page 605, 8th Edition, 2006.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200.
Kiran S. Kedlaya, Problem A-1, The 51th William Lowell Putnam Mathematical Competition, Dec 08 1990.
Loren Larson, Problem A-1, 51st Annual Putnam Competition, Math. Mag., 64 (1991), 141-144.
FORMULA
a(n) = (n+4)*a(n-1) - 4*n*a(n-2) + (4*n-8)*a(n-3) with a(0) = 2, a(1) = 3, a(2) = 6. - Dennis S. Kluk (mathemagician(AT)ameritech.net), Feb 12 2006
From Robert Israel, Mar 06 2016: (Start)
E.g.f.: 1/(1-x) + exp(2x). (End)
MAPLE
seq(2^n+n!, n=0..50); # Robert Israel, Mar 06 2016
MATHEMATICA
Table[n! + 2^n, {n, 0, 19}] (* Alonso del Arte, Mar 06 2016 *)
PROG
(Sage) [factorial(n)+2^n for n in range(0, 21)] # Zerinvary Lajos, Oct 27 2009
(Magma) [Factorial(n)+ 2^n: n in [0..30]]; // Vincenzo Librandi, Jun 10 2013
(PARI) a(n) = n! + 2^n; \\ Michel Marcus, Mar 30 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved