A223949 T(n,k)=Number of nXk 0..1 arrays with diagonals and antidiagonals unimodal and rows nondecreasing

2, 3, 4, 4, 9, 8, 5, 16, 27, 16, 6, 25, 54, 81, 32, 7, 36, 96, 177, 243, 64, 8, 49, 157, 321, 596, 729, 128, 9, 64, 241, 558, 1062, 2024, 2187, 256, 10, 81, 352, 928, 1821, 3645, 6869, 6561, 512, 11, 100, 494, 1479, 3115, 5951, 12856, 23285, 19683, 1024, 12, 121

Offset

1,1

Comments

Table starts

....2.....3......4......5......6.......7.......8.......9......10......11

....4.....9.....16.....25.....36......49......64......81.....100.....121

....8....27.....54.....96....157.....241.....352.....494.....671.....887

...16....81....177....321....558.....928....1479....2267....3356....4818

...32...243....596...1062...1821....3115....5233....8564...13613...21017

...64...729...2024...3645...5951....9919...16845...28558...47721...78071

..128..2187...6869..12856..20275...31899...52532...89135..152495..259230

..256..6561..23285..45626..71653..106838..166076..272997..464837..802560

..512.19683..78942.161604.257568..372791..545443..849070.1401993.2401956

.1024.59049.267681.571202.928047.1333858.1866509.2733557.4294573.7150718

Links

R. H. Hardin, Table of n, a(n) for n = 1..544

Formula

Empirical: columns k=1..7 have recurrences of order 1,1,5,10,16,24,33

Empirical: rows n=1..7 are polynomials of degree n for k>0,0,1,2,3,4,5

Example

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

Crossrefs

Column 1 is A000079

Column 2 is A000244

Row 1 is A000027(n+1)

Row 2 is A000290(n+1)

Sequence in context: A269619 A269435 A269656 * A224133 A228740 A269583

Adjacent sequences: A223946 A223947 A223948 * A223950 A223951 A223952

Keyword

nonn,tabl

Author

R. H. Hardin Mar 29 2013

Status

approved