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A052371 Triangle T(n,k) of n X n binary matrices with k=0...n^2 ones up to row and column permutations. 6
1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 6, 7, 7, 6, 3, 1, 1, 1, 1, 3, 6, 16, 21, 39, 44, 55, 44, 39, 21, 16, 6, 3, 1, 1, 1, 1, 3, 6, 16, 34, 69, 130, 234, 367, 527, 669, 755, 755, 669, 527, 367, 234, 130, 69, 34, 16, 6, 3, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..2890 (rows n=0..20)

EXAMPLE

Triangle begins:

1;

1, 1;

1, 1, 3, 1, 1;

1, 1, 3, 6, 7, 7, 6, 3, 1, 1;

1, 1, 3, 6, 16, 21, 39, 44, 55, 44, 39, 21, 16, 6, 3, 1, 1;

...

(the last block giving the numbers of 4 X 4 binary matrices with k=0..16 ones up to row and column permutations).

MATHEMATICA

permcount[v_] := Module[{m = 1, s = 0, t, i, k = 0}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t*k; s += t]; s!/m];

c[p_, q_] := Product[(1 + x^LCM[p[[i]], q[[j]]])^GCD[p[[i]], q[[j]]], {i, 1, Length[p]}, {j, 1, Length[q]}];

row[n_] := Module[{s = 0}, Do[Do[s += permcount[p]*permcount[q]*c[p, q], {q, IntegerPartitions[n]}], {p, IntegerPartitions[n]}]; CoefficientList[ s/(n!^2), x]]

row /@ Range[0, 5] // Flatten (* Jean-François Alcover, Sep 22 2019, after Andrew Howroyd *)

PROG

(PARI)

permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}

c(p, q)={prod(i=1, #p, prod(j=1, #q, (1 + x^lcm(p[i], q[j]))^gcd(p[i], q[j])))}

row(n)={my(s=0); forpart(p=n, forpart(q=n, s+=permcount(p) * permcount(q) * c(p, q))); Vec(s/(n!^2))}

for(n=1, 5, print(row(n))) \\ Andrew Howroyd, Nov 14 2018

CROSSREFS

Rows 6..8 are A052370, A053304, A053305.

Row sums are A002724.

Cf. A049311.

Sequence in context: A073780 A124389 A027023 * A062278 A260638 A268523

Adjacent sequences: A052368 A052369 A052370 * A052372 A052373 A052374

KEYWORD

nonn,tabf

AUTHOR

Vladeta Jovovic, Mar 08 2000

EXTENSIONS

a(0)=1 prepended by Andrew Howroyd, Nov 14 2018

STATUS

approved

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Last modified February 6 04:21 EST 2023. Contains 360097 sequences. (Running on oeis4.)