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

0,3

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

Formula

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

Prog

(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)}

Crossrefs

Column k=2 of A331160.

Cf. A000009, A219554, A331197.

Sequence in context: A240359 A282522 A329523 * A259664 A321880 A075673

Adjacent sequences: A331314 A331315 A331316 * A331318 A331319 A331320

Keyword

nonn

Author

Andrew Howroyd, Jan 13 2020

Status

approved