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
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Jul 27 2000
STATUS
approved