A225171 Triangle read by rows: T(n,k), 1 <= k <= n, is the number of non-degenerate fanout-free Boolean functions of n variables having AND rank k.

2, 4, 4, 32, 24, 8, 416, 304, 96, 16, 7552, 5440, 1760, 320, 32, 176128, 125824, 41280, 8000, 960, 64, 5018624, 3566080, 1180928, 237440, 31360, 2688, 128, 168968192, 119614464, 39875584, 8212736, 1146880, 111104, 7168, 256

Offset

1,1

Comments

Also the Bell transform of A225170. For the definition of the Bell transform see A264428. - Peter Luschny, Jan 29 2016

Links

Table of n, a(n) for n=1..36.

J. P. Hayes, Enumeration of fanout-free Boolean functions, J. ACM, 23 (1976), 700-709.

Index entries for sequences related to Boolean functions

Formula

Hayes (1976, Theorem 3) gives a recurrence.

Example

Triangle begins
2,
4,4,
32,24,8,
416,304,96,16,
7552,5440,1760,320,32,
176128,125824,41280,8000,960,64,
5018624,3566080,1180928,237440,31360,2688,128,
168968192,119614464,39875584,8212736,1146880,111104,7168,256,
...

Maple

# Function BellMatrix defined in A264428.
BellMatrix(n -> `if`(n=0, 2, add(combinat:-eulerian2(n, k)*2^(2*n-k), k=0..n)), 9); # Peter Luschny, Jan 29 2016

Mathematica

BellMatrix[f_Function, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
rows = 12;
M = BellMatrix[If[# == 0, 2, Sum[(#+k)!*Sum[(-1)^j/(k-j)!*Sum[(-1)^i*2^(# - i + j)*StirlingS1[# - i + j, j - i]/((# - i + j)!*i!), {i, 0, j}], {j, 1, k}], {k, 1, #}]]&, rows];
Table[M[[n, k]], {n, 2, rows}, {k, 2, n}] // Flatten (* Jean-François Alcover, Jun 24 2018, after Peter Luschny *)

Crossrefs

Columns give A225170 (or A005172), A005756, A224767, A224768.

Sequence in context: A371373 A092524 A137787 * A320600 A360685 A290606

Adjacent sequences: A225168 A225169 A225170 * A225172 A225173 A225174

Keyword

nonn,tabl

Author

N. J. A. Sloane, Apr 30 2013

Status

approved