login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A056090
Number of 4-element ordered antichain covers of an unlabeled n-element set.
4
25, 429, 3364, 17602, 71385, 242347, 720792, 1934076, 4777337, 11021713, 24008532, 49790614, 98954626, 189457350, 350941064, 631167840, 1105440045, 1890167329, 3162113836, 5185330818, 8348369731, 13215102985, 20593381200, 31626858540, 47916657405, 71681161365
OFFSET
4,1
REFERENCES
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)
V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
LINKS
K. S. Brown, Dedekind's problem
Eric Weisstein's World of Mathematics, Antichain covers
Index entries for linear recurrences with constant coefficients, signature (15, -105, 455, -1365, 3003, -5005, 6435, -6435, 5005, -3003, 1365, -455, 105, -15, 1).
FORMULA
a(n) = C(n + 14, 14) - 12*C(n + 10, 10) + 24*C(n + 8, 8) + 4*C(n + 7, 7) - 18*C(n + 6, 6) + 6*C(n + 5, 5) - 36*C(n + 4, 4) + 36*C(n + 3, 3) + 11*C(n + 2, 2) - 22*C(n + 1, 1) + 6*C(n, 0).
G.f.: x^4*(6*x^10 -62*x^9 +271*x^8 -636*x^7 +800*x^6 -328*x^5 -495*x^4 +812*x^3 -446*x^2 +54*x +25)/(1-x)^15. - Colin Barker, May 29 2012
a(n) = (-104270181120 n + 236073062016 n^2 - 169534943760 n^3 + 28403538800 n^4 + 12862329480 n^5 - 2983956976 n^6 - 613678065 n^7 + 39763295 n^8 + 21456435 n^9 + 2461459 n^10 + 143325 n^11 + 5005 n^12 + 105 n^13 + n^14)/(14)!. - G. C. Greubel, Oct 06 2017
MATHEMATICA
Table[(-104270181120 n + 236073062016 n^2 - 169534943760 n^3 + 28403538800 n^4 + 12862329480 n^5 - 2983956976 n^6 - 613678065 n^7 + 39763295 n^8 + 21456435 n^9 + 2461459 n^10 + 143325 n^11 + 5005 n^12 + 105 n^13 + n^14)/(14)!, {n, 4, 50}] (* G. C. Greubel, Oct 06 2017 *)
LinearRecurrence[{15, -105, 455, -1365, 3003, -5005, 6435, -6435, 5005, -3003, 1365, -455, 105, -15, 1}, {25, 429, 3364, 17602, 71385, 242347, 720792, 1934076, 4777337, 11021713, 24008532, 49790614, 98954626, 189457350, 350941064}, 30] (* Harvey P. Dale, Dec 09 2021 *)
PROG
(PARI) for(n=4, 50, print1((-104270181120*n + 236073062016*n^2 - 169534943760*n^3 + 28403538800*n^4 + 12862329480*n^5 - 2983956976*n^6 - 613678065*n^7 + 39763295*n^8 + 21456435*n^9 + 2461459*n^10 + 143325*n^11 + 5005*n^12 + 105*n^13 + n^14)/(14)!, ", ")) \\ G. C. Greubel, Oct 06 2017
(Magma) [(-104270181120*n + 236073062016*n^2 - 169534943760*n^3 + 28403538800*n^4 + 12862329480*n^5 - 2983956976*n^6 - 613678065*n^7 + 39763295*n^8 + 21456435*n^9 + 2461459*n^10 + 143325*n^11 + 5005*n^12 + 105*n^13 + n^14)/Factorial(14): n in [4..50]]; // G. C. Greubel, Oct 06 2017
CROSSREFS
Cf. A056047 for 4-antichain (unordered) covers of a labeled n-set, A051112. See also A056074, A056093.
Sequence in context: A226712 A020577 A021714 * A020448 A203544 A021704
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Jul 27 2000
STATUS
approved