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A051112 Number of monotone Boolean functions of n variables with 4 mincuts. Also Sperner systems with 4 blocks. 44
0, 0, 0, 0, 25, 2020, 82115, 2401910, 58089465, 1245331920, 24625121455, 460316430970, 8266174350005, 144171200793620, 2461016066613195, 41343340015862430, 686274244801356145, 11289648429330100120 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

REFERENCES

J. L. Arocha, Antichains in ordered sets, (in Spanish) An. Inst. Mat. UNAM, vol. 27, 1987, 1-21.

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 293, #8, s(n,4).

D. M. Cvetkovic, The number of antichains of finite power sets, Publ. Inst. Math., 13 (27), 1972, 5-9.

V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean function, Belgrade, 1999, in preparation.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 0..831 (next term has 1001 digits)

K. S. Brown, Dedekind's Problem

Vladeta Jovovic, Illustration for A016269, A047707, A051112-A051118

Index entries for sequences related to Boolean functions

Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.

Index entries for linear recurrences with constant coefficients, signature (82, -2970, 62700, -856713, 7947786, -51019100, 226259000, -678011136, 1304341632, -1445575680, 696729600).

FORMULA

(1/4!)*(16^n - 12*12^n + 24*10^n + 4*9^n - 18*8^n + 6*7^n - 36*6^n + 36*5^n + 11*4^n - 22*3^n + 6*2^n)

a(n)=82*a(n - 1) - 2970*a(n - 2) + 62700*a(n - 3) - 856713*a(n - 4) + 7947786*a(n - 5) - 51019100*a(n - 6) + 226259000*a(n - 7) - 678011136*a(n - 8) + 1304341632*a(n - 9) - 1445575680*a(n - 10) + 696729600*a(n - 11)

G.f.: 5x^4(5-6x-1855x^2+20076x^3-44356x^4-215280x^5+759168x^6) / ((1-3x)(1-4x)(1-5x)(1-6x)(1-2x)(1-7x)(1-8x)(1-9x)(1-10x)(1-12x)(1-16x))

MATHEMATICA

(1/4!)*(16^n-12*12^n+24*10^n+4*9^n-18*8^n+6*7^n-36*6^n+36*5^n+11*4^n-22*3^n+6*2^n), {n, 0, 20}] (* or *) LinearRecurrence[{82, -2970, 62700, -856713, 7947786, -51019100, 226259000, -678011136, 1304341632, -1445575680, 696729600}, {0, 0, 0, 0, 25, 2020, 82115, 2401910, 58089465, 1245331920, 24625121455}, 20] (* Harvey P. Dale, Nov 26 2019 *)

PROG

(PARI) a(n)=(16^n-12*12^n+24*10^n+4*9^n-18*8^n+6*7^n-36*6^n+36*5^n+11*4^n -22*3^n+6*2^n)/24 \\ Charles R Greathouse IV, Mar 14 2012

CROSSREFS

Cf. A016269, A047707, A051113-A051118.

Sequence in context: A056047 A281436 A197671 * A061843 A173948 A279276

Adjacent sequences:  A051109 A051110 A051111 * A051113 A051114 A051115

KEYWORD

nonn,easy,nice

AUTHOR

Vladeta Jovovic, Goran Kilibarda, Zoran Maksimovic

EXTENSIONS

Recurrence and g.f. from Michael Somos

STATUS

approved

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Last modified April 18 05:44 EDT 2021. Contains 343072 sequences. (Running on oeis4.)