A080568 Sum of the Fibonacci numbers A000045 and the factorials A000142.

1, 2, 3, 8, 27, 125, 728, 5053, 40341, 362914, 3628855, 39916889, 479001744, 6227021033, 87178291577, 1307674368610, 20922789888987, 355687428097597, 6402373705730584, 121645100408836181, 2432902008176646765, 51090942171709450946, 1124000727777607697711

Offset: 0

Author

Alasdair Kergon (agk(AT)oxlug.org), Feb 21 2003

Keywords

• easy
• nonn

Comments

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.

References

• Cambridge Archimedeans' Problems Drive, 2001.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A000045, A000142.

Programs

Magma

[Factorial(n)+Fibonacci(n): n in [0..25]]; // Vincenzo Librandi, May 03 2011

Maple

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

Mathematica

Table[n!+Fibonacci[n],{n,0,100}] (* Vladimir Joseph Stephan Orlovsky, May 02 2011 *)

PARI

vector(30, n, n--; n! + fibonacci(n)) \\ Michel Marcus, Jul 05 2015

Formula

E.g.f.: (2/sqrt(5))*exp(x/2)*sinh(sqrt(5)*x/2)+1/(1-x). - Alois P. Heinz, Jul 05 2015