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 A051303 Number of 3-element proper antichains of an n-element set. 4
 0, 0, 0, 1, 30, 605, 9030, 110901, 1200150, 11932285, 111885510, 1006471301, 8786447670, 75039565965, 630534185190, 5234341175701, 43059373189590, 351805681631645, 2859550165976070, 23152657123816101, 186907026783617910, 1505512392025329325 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (29,-343,2135,-7504,14756,-14832,5760). FORMULA a(n) = (8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2)/3!. G.f.: x^3*(360*x^3-78*x^2-x-1) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(8*x-1)). - Colin Barker, Nov 27 2012 a(n) = 29*a(n-1) - 343*a(n-2) + 2135*a(n-3) - 7504*a(n-4) + 14756*a(n-5) - 14832*a(n-6) + 5760*a(n-7) for n > 6. - Wesley Ivan Hurt, Oct 06 2017 MAPLE A051303:=n->(8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2)/3!: seq(A051303(n), n=0..30); # Wesley Ivan Hurt, Oct 06 2017 MATHEMATICA Table[(8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2)/3!, {n, 0, 25}] (* G. C. Greubel, Oct 06 2017 *) PROG (PARI) for(n=0, 25, print1((8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2 )/3!, ", ")) \\ G. C. Greubel, Oct 06 2017 (MAGMA) [(8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2)/3!: n in [0..25]]; // G. C. Greubel, Oct 06 2017 CROSSREFS Cf. A032263, A036239, A051112. Sequence in context: A024436 A042744 A020980 * A020975 A277877 A279870 Adjacent sequences:  A051300 A051301 A051302 * A051304 A051305 A051306 KEYWORD nonn,easy AUTHOR Vladeta Jovovic, Goran Kilibarda, Zoran Maksimovic STATUS approved

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Last modified December 9 08:41 EST 2021. Contains 349627 sequences. (Running on oeis4.)