A204651 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) nondecreasing in column and row directions, respectively.

8, 16, 16, 28, 32, 28, 48, 56, 56, 48, 80, 90, 104, 90, 80, 132, 137, 178, 178, 137, 132, 216, 200, 284, 330, 284, 200, 216, 352, 283, 434, 571, 571, 434, 283, 352, 572, 390, 637, 938, 1076, 938, 637, 390, 572, 928, 526, 908, 1478, 1918, 1918, 1478, 908, 526, 928

Offset: 1

Author

R. H. Hardin Jan 17 2012

Keywords

• nonn
• tabl

Comments

Table starts

...8..16..28...48...80...132...216...352...572....928...1504...2436...3944

..16..32..56...90..137...200...283...390...526....696....906...1162...1471

..28..56.104..178..284...434...637...908..1259...1708...2270...2966...3814

..48..90.178..330..571...938..1478..2248..3317...4766...6690...9198..12415

..80.137.284..571.1076..1918..3261..5329..8408..12867..19162..27859..39640

.132.200.434..938.1918..3702..6780.11868.19969..32450..51134..78404.117324

.216.283.637.1478.3261..6780.13314.24862.44426..76378.126906.204583.321038

.352.390.908.2248.5329.11868.24862.49312.93219.168960.295101.498776.818748

Examples

			Some solutions for n=5 k=3
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..1....0..0..0..1
..0..0..0..0....0..0..0..1....0..0..0..1....0..0..0..1....0..0..1..1
..0..0..0..0....0..0..0..1....0..0..0..1....0..0..0..1....0..0..1..1
..0..0..1..1....0..0..1..1....0..0..0..1....0..0..0..1....0..0..1..1
..0..0..1..1....1..1..1..1....0..0..0..1....0..0..0..1....0..1..1..1
..0..0..1..1....1..1..1..1....1..1..1..0....0..1..1..1....0..1..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..6956

Formula

Empirical: T(n,k) recurrences

T(1,k)=2*T(1,k-1)-T(1,k-3)

T(2,k)=4*T(2,k-1)-5*T(2,k-2)+5*T(2,k-4)-4*T(2,k-5)+T(2,k-6)

T(3,k)=4*T(3,k-1)-5*T(3,k-2)+5*T(3,k-4)-4*T(3,k-5)+T(3,k-6) for k>7

T(4,k)=5*T(4,k-1)-9*T(4,k-2)+5*T(4,k-3)+5*T(4,k-4)-9*T(4,k-5)+5*T(4,k-6)-T(4,k-7) for k>9

and in general for n>2 (checked to n=15 k=210):

row recurrence coefficients are the coefficients of (1+x)*(1-x)^(k+2) and the row recurrence is valid for k>2*n+1