A224133 T(n,k)=Number of nXk 0..1 arrays with rows nondecreasing and antidiagonals unimodal

2, 3, 4, 4, 9, 8, 5, 16, 27, 16, 6, 25, 58, 81, 32, 7, 36, 106, 208, 243, 64, 8, 49, 175, 419, 748, 729, 128, 9, 64, 269, 760, 1635, 2692, 2187, 256, 10, 81, 392, 1279, 3149, 6392, 9688, 6561, 512, 11, 100, 548, 2032, 5648, 12874, 25047, 34864, 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.....58.....106.....175.....269......392......548......741......975

...16....81....208.....419.....760....1279.....2032.....3083.....4504.....6375

...32...243....748....1635....3149....5648.....9577....15505....24141....36350

...64...729...2692....6392...12874...24095....42832....72888...119424...189263

..128..2187...9688...25047...52581..101412...186348...329167...561329...927323

..256..6561..34864...98221..215136..425246...799954..1452236..2554044..4361910

..512.19683.125464..385194..881461.1783229..3414588..6323696.11385356.19962630

.1024.59049.451504.1510527.3613806.7484923.14548514.27345986.50113246.89697284

Links

R. H. Hardin, Table of n, a(n) for n = 1..1009

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1)

k=3: a(n) = 4*a(n-1) -2*a(n-2) +2*a(n-3)

k=4: a(n) = 5*a(n-1) -5*a(n-2) +2*a(n-3) +4*a(n-4)

k=5: a(n) = 6*a(n-1) -9*a(n-2) +4*a(n-3) +2*a(n-4) +8*a(n-5)

k=6: a(n) = 7*a(n-1) -14*a(n-2) +9*a(n-3) +4*a(n-5) +16*a(n-6)

k=7: a(n) = 8*a(n-1) -20*a(n-2) +18*a(n-3) -4*a(n-4) +2*a(n-5) +8*a(n-6) +32*a(n-7)

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
..1..1..1..1....0..0..1..1....0..0..0..1....0..1..1..1....0..1..1..1
..0..1..1..1....1..1..1..1....1..1..1..1....1..1..1..1....0..1..1..1
..0..0..0..0....1..1..1..1....0..0..0..1....0..0..0..0....0..0..0..0

Crossrefs

Column 1 is A000079

Column 2 is A000244

Row 1 is A000027(n+1)

Row 2 is A000290(n+1)

Sequence in context: A269435 A269656 A223949 * A228740 A269583 A250361

Adjacent sequences: A224130 A224131 A224132 * A224134 A224135 A224136

Keyword

nonn,tabl

Author

R. H. Hardin Mar 31 2013

Status

approved