|
%I #17 Sep 08 2022 08:45:09
%S 1,2,3,8,27,125,728,5053,40341,362914,3628855,39916889,479001744,
%T 6227021033,87178291577,1307674368610,20922789888987,355687428097597,
%U 6402373705730584,121645100408836181,2432902008176646765,51090942171709450946,1124000727777607697711
%N Sum of the Fibonacci numbers A000045 and the factorials A000142.
%C Original puzzle was to find the next four terms after 2, 3, 8, 27, 125. The cubes were intended to mislead - providing one further term would have made the intended sequence too obvious.
%D Cambridge Archimedeans' Problems Drive, 2001.
%H Vincenzo Librandi, <a href="/A080568/b080568.txt">Table of n, a(n) for n = 0..100</a>
%F E.g.f.: (2/sqrt(5))*exp(x/2)*sinh(sqrt(5)*x/2)+1/(1-x). - _Alois P. Heinz_, Jul 05 2015
%p with(combstruct): with(combinat): a:=proc(m) [ZL, {ZL=Set(Cycle(Z, card>=m))}, labeled]; end: ZLL:=a(1): seq(count(ZLL, size=n)+fibonacci(n), n=0..19); # _Zerinvary Lajos_, Jun 11 2008
%t Table[n!+Fibonacci[n],{n,0,100}] (* _Vladimir Joseph Stephan Orlovsky_, May 02 2011 *)
%o (Magma) [Factorial(n)+Fibonacci(n): n in [0..25]]; // _Vincenzo Librandi_, May 03 2011
%o (PARI) vector(30, n, n--; n! + fibonacci(n)) \\ _Michel Marcus_, Jul 05 2015
%Y Cf. A000045, A000142.
%K easy,nonn
%O 0,2
%A Alasdair Kergon (agk(AT)oxlug.org), Feb 21 2003
|
