OFFSET
0,1
COMMENTS
For n>=0, a(n) is equal to the number of functions f:{1,2,3,4,5}->{1,2,...,n+2} such that Im(f) contains 2 fixed elements. - Aleksandar M. Janjic and Milan Janjic, Feb 24 2007
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
O. Bagdasar, On some functions involving the lcm and gcd of integer tuples, Scientific Publications of the State University of Novi Pazar, Appl. Maths. Inform. and Mech., Vol. 6, 2 (2014), 91--100.
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+2)^5-2*(n+1)^5+n^5.
a(n) = 30*A005900(n+1). - R. J. Mathar, Sep 02 2008
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Colin Barker, Dec 13 2014
G.f.: 30*(x+1)^2 / (x-1)^4. - Colin Barker, Dec 13 2014
MATHEMATICA
Table[20*n^3 + 10*n, {n, 1, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 19 2011 *)
Differences[#[[2]]-#[[1]]&/@Partition[Range[0, 40]^5, 2, 1]] (* or *) LinearRecurrence[{4, -6, 4, -1}, {30, 180, 570, 1320}, 40] (* Harvey P. Dale, Jun 05 2019 *)
PROG
(PARI) Vec(30*(x+1)^2 / (x-1)^4 + O(x^100)) \\ Colin Barker, Dec 13 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eli McGowan (ejmcgowa(AT)mail.lakeheadu.ca), Mar 25 2002
STATUS
approved