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

1,1

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

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

Example

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

Crossrefs

Sequence in context: A040056 A242890 A224550 * A203452 A363982 A319317

Adjacent sequences: A204648 A204649 A204650 * A204652 A204653 A204654

Keyword

nonn,tabl

Author

R. H. Hardin Jan 17 2012

Status

approved