This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A056074 #27 Feb 16 2025 08:32:43
%S A056074 2,17,71,212,518,1106,2142,3852,6534,10571,16445,24752,36218,51716,
%T A056074 72284,99144,133722,177669,232883,301532,386078,489302,614330,764660,
%U A056074 944190,1157247,1408617,1703576
%N A056074 Number of 3-element ordered antichain covers of an unlabeled n-element set.
%D A056074 V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)
%D A056074 V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
%H A056074 G. C. Greubel, <a href="/A056074/b056074.txt">Table of n, a(n) for n = 3..1000</a>
%H A056074 K. S. Brown, <a href="http://www.mathpages.com/home/kmath515.htm">Dedekind's problem</a>
%H A056074 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Cover.html">Antichain covers</a>
%H A056074 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
%F A056074 a(n) = C(n + 6, 6) - 6*C(n + 4, 4) + 6*C(n + 3, 3) + 3*C(n + 2, 2) - 6*C(n + 1, 1) + 2*C(n, 0).
%F A056074 a(0)=2, a(1)=17, a(2)=71, a(3)=212, a(4)=518, a(5)=1106, a(6)=2142, a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). - _Harvey P. Dale_, Jul 12 2011
%F A056074 G.f.: (-2-3*x+6*x^2-2*x^3)/(x-1)^7. - _Harvey P. Dale_, Jul 12 2011
%F A056074 a(n) = n*(n^5 + 21*n^4 - 5*n^3 - 345*n^2 + 724*n - 396)/720. - _Charles R Greathouse IV_, Feb 19 2017
%p A056074 A056074:=n->n*(n^5 + 21*n^4 - 5*n^3 - 345*n^2 + 724*n - 396)/720: seq(A056074(n), n=3..60); # _Wesley Ivan Hurt_, Oct 06 2017
%t A056074 LinearRecurrence[{7,-21,35,-35,21,-7,1},{2,17,71,212,518,1106,2142},30] (* or *) Table[Binomial[n+6,6]-6Binomial[n+4,4]+6Binomial[n+3,3]+ 3Binomial[n+2,2]- 6Binomial[n+1,1]+ 2Binomial[n,0],{n,3,30}] (* _Harvey P. Dale_, Jul 12 2011 *)
%o A056074 (PARI) a(n)=n*(n^5 + 21*n^4 - 5*n^3 - 345*n^2 + 724*n - 396)/720 \\ _Charles R Greathouse IV_, Feb 19 2017
%o A056074 (Magma) [n*(n^5 + 21*n^4 - 5*n^3 - 345*n^2 + 724*n - 396)/720: n in [3..25]]; // _G. C. Greubel_, Oct 06 2017
%Y A056074 Cf. A056046 for 3-antichain (unordered) covers of a labeled n-set, A047707. See also A056090, A056093.
%K A056074 nonn,nice,easy
%O A056074 3,1
%A A056074 _Vladeta Jovovic_, Goran Kilibarda, Jul 26 2000