A094792 a(n) = (1/n!)*A001565(n).

2, 11, 32, 71, 134, 227, 356, 527, 746, 1019, 1352, 1751, 2222, 2771, 3404, 4127, 4946, 5867, 6896, 8039, 9302, 10691, 12212, 13871, 15674, 17627, 19736, 22007, 24446, 27059, 29852, 32831, 36002, 39371, 42944, 46727, 50726, 54947, 59396, 64079

Offset: 0

Author

Benoit Cloitre, Jun 11 2004

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A001563, A001564, A001565, A001688, A001689, A023043.

Cf. A094791, A094793, A094794, A094795.

Programs

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 *)

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