OFFSET
0,1
COMMENTS
Number of injections from {1,2,3} to {1,2,...,n} with no fixed points. - Fiona T. Brunk (fbrunk(AT)mcs.st-and.ac.uk), May 23 2006
LINKS
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = n^3 + 3*n^2 + 5*n + 2.
a(n) = Sum_{i=0..3} (-1)^i*binomial(3,i)*(n-i)!/(n-3)!. - Fiona T. Brunk (fbrunk(AT)mcs.st-and.ac.uk), May 23 2006
G.f.: (x^3+3*x+2) / (x-1)^4. - Colin Barker, Jun 15 2013
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Fung Lam, Apr 17 2014
P-recursive: n*a(n) = (n+4)*a(n-1) - a(n-2) with a(0) = 2 and a(1) = 11. Cf. A094791. - Peter Bala, Jul 25 2021
MAPLE
with(combinat):seq(fibonacci(4, i)-1, i=1..40); # Zerinvary Lajos, Mar 20 2008
MATHEMATICA
Table[n^3+3*n^2+5*n+2, {n, 0, 70}] (* Vladimir Joseph Stephan Orlovsky, May 04 2011 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Jun 11 2004
STATUS
approved