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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 1 is A000302

Column 2 is A001025

Row 1 is A223659

Row 2 is A223756

Sequence in context: A223850 A223663 A224113 * A223801 A336938 A232516

Adjacent sequences: A223873 A223874 A223875 * A223877 A223878 A223879

Keyword

nonn,tabl

Author

R. H. Hardin Mar 28 2013

Status

approved