OFFSET
0,4
COMMENTS
The paper by G. Kilibarda, Enumeration of certain classes of antichains, Publications de l'Institut Mathematique, Nouvelle série, 97 (111) (2015), mentions many sequences, but since only very condensed formulas are given, it is hard to match them with entries in the OEIS. It would be nice to add this reference to all the sequences that it mentions. - N. J. A. Sloane, Jan 01 2016
Term a(1108) has 1000 decimal digits. - Michael De Vlieger, Jan 26 2016
REFERENCES
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 292, #8, s(n,3).
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..1107
K. S. Brown, Dedekind's problem.
Vladeta Jovovic, Illustration for A016269, A047707, A051112-A051118
G. Kilibarda, Enumeration of certain classes of antichains, Publications de l'Institut Mathematique, Nouvelle série, 97 (111) (2015), 69-87 DOI: 10.2298/PIM140406001K. See page 86, formula for alpha^hat(3,n).
Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.
Index entries for linear recurrences with constant coefficients, signature (28,-315,1820,-5684,9072,-5760).
FORMULA
a(n) = (2^n)*(2^n - 1)*(2^n - 2)/6 - (6^n - 5^n - 4^n + 3^n).
G.f.: -2*x^3*(36*x^2-4*x-1)/((2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(8*x-1)). - Colin Barker, Jul 31 2012
a(n) = Binomial(2^n,3) - (6^n - 5^n - 4^n + 3^n). - Ross La Haye, Jan 26 2016
MATHEMATICA
Table[Binomial[2^n, 3] - (6^n - 5^n - 4^n + 3^n), {n, 20}] (* or *)
CoefficientList[Series[-2 x^3 (36 x^2 - 4 x - 1)/((2 x - 1) (3 x - 1) (4 x - 1) (5 x - 1) (6 x - 1) (8 x - 1)), {x, 0, 20}], x] (* Michael De Vlieger, Jan 26 2016 *)
PROG
(PARI) a(n)=binomial(2^n, 3)-(6^n-5^n-4^n+3^n) \\ Charles R Greathouse IV, Apr 08 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved