login
T(n,k)=Number of (n+1)X(k+1) 0..1 arrays x(i,j) with row sums sum{j^4*x(i,j), j=1..k+1} nondecreasing, and column sums sum{i^4*x(i,j), i=1..n+1} nondecreasing
9

%I #4 Nov 30 2013 09:45:46

%S 7,14,14,25,45,25,41,130,130,41,63,336,650,336,63,92,785,2942,2942,

%T 785,92,124,1682,11819,24520,11819,1682,124,164,3147,42305,183010,

%U 183010,42305,3147,164,212,5503,127788,1202234,2625117,1202234,127788,5503,212

%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays x(i,j) with row sums sum{j^4*x(i,j), j=1..k+1} nondecreasing, and column sums sum{i^4*x(i,j), i=1..n+1} nondecreasing

%C Table starts

%C ...7....14......25........41...........63.............92.............124

%C ..14....45.....130.......336..........785...........1682............3147

%C ..25...130.....650......2942........11819..........42305..........127788

%C ..41...336....2942.....24520.......183010........1202234.........6552283

%C ..63...785...11819....183010......2625117.......33345183.......349972980

%C ..92..1682...42305...1202234.....33345183......836488618.....17452506031

%C .124..3147..127788...6552283....349972980....17452506031....738302560541

%C .164..5503..340647..30323734...3057451085...300697300448..25786803621594

%C .212..9093..812254.119567288..22080850326..4213428870171.728236411637198

%C .270.14712.1845329.429359835.139531590875.50295798679859

%H R. H. Hardin, <a href="/A232797/b232797.txt">Table of n, a(n) for n = 1..126</a>

%e Some solutions for n=4 k=4

%e ..1..0..1..0..0....0..0..0..0..0....0..1..1..1..0....0..0..0..0..0

%e ..1..0..0..1..0....1..0..1..0..0....0..1..1..1..0....0..0..0..0..0

%e ..0..0..1..0..1....0..1..0..1..0....1..1..0..0..1....1..1..1..0..1

%e ..1..0..0..1..1....0..0..1..1..0....0..0..0..1..1....1..0..0..1..1

%e ..0..1..1..1..1....0..0..0..0..1....0..0..1..1..1....0..1..1..1..1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 30 2013