A268523 Irregular triangle read by rows: T(n,i) = number of n X n semi-canonical binary matrices with exactly i 1’s, where 0 <= i <= n^2.

1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 8, 10, 9, 8, 3, 1, 1, 1, 1, 3, 8, 25, 49, 84, 107, 121, 101, 72, 41, 24, 8, 3, 1, 1, 1, 1, 3, 8, 25, 80, 220, 524, 1057, 1806, 2671, 3365, 3680, 3468, 2865, 2072, 1314, 723, 362, 166, 72, 24, 8, 3, 1, 1, 1, 1, 3, 8, 25, 80, 283, 925, 2839, 7721, 18590, 39522, 74677, 125449, 188290, 252954, 305561, 332402, 326650, 290171, 233656, 170704, 113448, 68677, 37996, 19188, 8910, 3847, 1588, 613, 299, 72, 24, 8, 3, 1

Offset

0,5

Links

Table of n, a(n) for n=0..95.

K. Yordzhev, Semi-canonical binary matrices, arXiv preprint arXiv:1506.04642 [math.CO], 2015.

Example

Triangle begins:
1,1,
1,1,3,1,1,
1,1,3,8,10,9,8,3,1,1,
1,1,3,8,25,49,84,107,121,101,72,41,24,8,3,1,1,
1,1,3,8,25,80,220,524,1057,1806,2671,3365,3680,3468,2865,2072,1314,723,362,166,72,24,8,3,1,1,
...

Crossrefs

Sequence in context: A052371 A062278 A260638 * A195768 A016465 A122947

Adjacent sequences: A268520 A268521 A268522 * A268524 A268525 A268526

Keyword

nonn,tabf

Author

N. J. A. Sloane, Feb 12 2016

Status

approved