A085539 a(n) = n^6 - n^5.

0, 0, 32, 486, 3072, 12500, 38880, 100842, 229376, 472392, 900000, 1610510, 2737152, 4455516, 6991712, 10631250, 15728640, 22717712, 32122656, 44569782, 60800000, 81682020, 108226272, 141599546, 183140352, 234375000, 297034400, 373071582, 464679936

Offset: 0

Author

N. J. A. Sloane, Jul 05 2003

Keywords

• nonn
• easy

Comments

For n>=1, a(n) is equal to the number of functions f:{1,2,3,4,5,6}->{1,2,...,n} such that for a fixed x in {1,2,3,4,5,6} and a fixed y in {1,2,...,n} we have f(x)<>y. - Aleksandar M. Janjic and Milan Janjic, Mar 13 2007

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

A diagonal of A228273.

Cf. A000584, A001014.

Programs

Magma

[n^6-n^5: n in [0..40]]; // Vincenzo Librandi, Aug 15 2016

Mathematica

f[n_]:=n^6-n^5;f[Range[0,60]] (* Vladimir Joseph Stephan Orlovsky, Feb 10 2011 *)
Table[n^6 - n^5, {n, 0, 50}] (* Vincenzo Librandi, Aug 15 2016 *)

PARI

a(n)=n^6-n^5 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: -2*x^2*(x^4+41*x^3+171*x^2+131*x+16)/(x-1)^7. - Colin Barker, Nov 06 2012

Sum_{n>=2} 1/a(n) = 5 - Sum_{k=2..5} zeta(k). - Amiram Eldar, Jul 05 2020