A250544 T(n,k) = number of (n+1)X(k+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)-x(i-1,j) in the j direction.

150, 1080, 1080, 6627, 10704, 6627, 36552, 79366, 79366, 36552, 187000, 491650, 644779, 491650, 187000, 905440, 2701872, 4169584, 4169584, 2701872, 905440, 4206453, 13657024, 23289547, 27240292, 23289547, 13657024, 4206453, 18933408

Offset: 1

Author

R. H. Hardin, Nov 24 2014

Keywords

• nonn
• tabl

Comments

Peter Luschny remarks that the coefficients of the empirical recurrence relation for the column 1 are listed in the 9th row of A246117. - M. F. Hasler, Feb 11 2015

Examples

			Some solutions for n=2 k=4
..2..2..1..0..0....2..0..3..1..1....2..2..2..2..0....0..0..2..0..0
..2..3..2..2..2....0..0..3..2..2....2..2..2..2..0....1..1..3..1..1
..1..3..2..3..3....0..0..3..2..3....1..2..2..2..3....0..0..2..0..2
Table starts:
.......150.......1080........6627........36552........187000........905440
......1080......10704.......79366.......491650.......2701872......13657024
......6627......79366......644779......4169584......23289547.....117777788
.....36552.....491650.....4169584.....27240292.....151170400.....752602024
....187000....2701872....23289547....151170400.....824599694....4013192386
....905440...13657024...117777788....752602024....4013192386...19031828420
...4206453...64993652...555362165...3475227442...18064444143...83356429646
..18933408..295871112..2489782728..15210145612...76961701472..345394150196
..83153850.1302924116.10756619019..64036997144..315204675572.1375930596944
.358250280.5595784456.45218540866.262068107390.1254564769204.5328628464360
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..144

Crossrefs

Row/column 1 is A223069(n+1) and row/column 2 of A223071.

Row/column 2-7 are A250538 - A250543; diagonal is A250537.

See also A250676, A250669 - A250675, A250691, A250692...

Formula

Empirical for column k (k=2-7 recurrence also works for k=1):

k=1: a(n) = 16*a(n-1) -106*a(n-2) +376*a(n-3) -769*a(n-4) +904*a(n-5) -564*a(n-6) +144*a(n-7)

k=2: [order 16, see A250538]

k=3: [same order 16]

k=4: [same order 16]

k=5: [same order 16]

k=6: [same order 16]

k=7: [same order 16]

Extensions

Edited by M. F. Hasler, Feb 11 2015