

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,j1) and c(i,j)=a(i,j)+a(i1,j) nondecreasing in column and row directions, respectively


9



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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



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



FORMULA

Empirical: T(n,k) recurrences
T(1,k)=2*T(1,k1)T(1,k3)
T(2,k)=4*T(2,k1)5*T(2,k2)+5*T(2,k4)4*T(2,k5)+T(2,k6)
T(3,k)=4*T(3,k1)5*T(3,k2)+5*T(3,k4)4*T(3,k5)+T(3,k6) for k>7
T(4,k)=5*T(4,k1)9*T(4,k2)+5*T(4,k3)+5*T(4,k4)9*T(4,k5)+5*T(4,k6)T(4,k7) for k>9
and in general for n>2 (checked to n=15 k=210):
row recurrence coefficients are the coefficients of (1+x)*(1x)^(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



KEYWORD



AUTHOR



STATUS

approved



