A331317 Number of nonnegative integer matrices with 2 distinct columns and any number of distinct nonzero rows with each column sum being n and rows in decreasing lexicographic order.

0, 1, 4, 15, 44, 120, 319, 804, 1960, 4652, 10782, 24435, 54329, 118663, 254969, 539825, 1127247, 2323811, 4733634, 9535025, 19005218, 37507726, 73333405, 142112298, 273092198, 520612163, 984943887, 1849920530, 3450475858, 6393203485, 11770416017, 21538245911, 39181212114

Offset: 0

Author

Andrew Howroyd, Jan 13 2020

Keywords

• nonn

Comments

The condition that the rows be in decreasing order is equivalent to considering nonequivalent matrices with distinct rows up to permutation of rows.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..400

Crossrefs

Column k=2 of A331160.

Cf. A000009, A219554, A331197.

Programs

PARI

a(n)={my(p=prod(i=0, n, prod(j=0, n, 1 + x^i*y^j + O(x*x^n) + O(y*y^n))), q=prod(i=1, n, 1 + x^i + O(x*x^n))); polcoef(polcoef(p,n), n)/2 - polcoef(q,n)}

Formula

a(n) = A219554(n) - A000009(n).