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A080568 Sum of the Fibonacci numbers A000045 and the factorials A000142. 2
1, 2, 3, 8, 27, 125, 728, 5053, 40341, 362914, 3628855, 39916889, 479001744, 6227021033, 87178291577, 1307674368610, 20922789888987, 355687428097597, 6402373705730584, 121645100408836181, 2432902008176646765, 51090942171709450946, 1124000727777607697711 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

FORMULA

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

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 *)

PROG

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

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

CROSSREFS

Cf. A000045, A000142.

Sequence in context: A121401 A318895 A093858 * A091339 A006277 A186927

Adjacent sequences:  A080565 A080566 A080567 * A080569 A080570 A080571

KEYWORD

easy,nonn

AUTHOR

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

STATUS

approved

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Last modified September 21 12:35 EDT 2019. Contains 327253 sequences. (Running on oeis4.)