A056090 Number of 4-element ordered antichain covers of an unlabeled n-element set.

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

G. C. Greubel, Table of n, a(n) for n = 4..1000

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

Adjacent sequences: A056087 A056088 A056089 * A056091 A056092 A056093

Keyword

nonn

Author

Vladeta Jovovic, Goran Kilibarda, Jul 27 2000

Status

approved