A223876 T(n,k)=Number of nXk 0..3 arrays with rows, diagonals and antidiagonals unimodal.

4, 16, 16, 50, 256, 64, 130, 2500, 4096, 256, 296, 16900, 99223, 65536, 1024, 610, 87616, 1336985, 3863372, 1048576, 4096, 1163, 372100, 12520369, 88682677, 152918517, 16777216, 16384, 2083, 1352569, 90648289, 1271992512, 5941888105

Offset: 1

Author

R. H. Hardin Mar 28 2013

Keywords

• nonn
• tabl

Comments

Table starts

.......4............16................50..................130

......16...........256..............2500................16900

......64..........4096.............99223..............1336985

.....256.........65536...........3863372.............88682677

....1024.......1048576.........152918517...........5941888105

....4096......16777216........6066668157.........411716468431

...16384.....268435456......240345697904.......28928809433978

...65536....4294967296.....9519219712534.....2033941972287214

..262144...68719476736...377068749332794...142745781634483746

.1048576.1099511627776.14936662560715369.10010372252279889400

Examples

			Some solutions for n=3 k=4
..0..0..0..1....0..0..0..3....0..2..3..3....0..0..0..2....0..0..0..0
..2..2..2..3....2..2..3..3....2..2..3..1....0..2..2..2....0..0..0..3
..2..3..1..1....0..1..2..3....1..1..3..1....2..2..2..1....1..1..3..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..97

Crossrefs

Column 1 is A000302

Column 2 is A001025

Row 1 is A223659

Row 2 is A223756

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1)

k=2: a(n) = 16*a(n-1)

k=3: [recurrence of order 28]

Empirical: rows n=1..4 are polynomials of degree 6*n for k>0,0,1,10