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%I #27 May 05 2022 04:44:51
%S 2,3,3,4,7,4,5,14,14,5,6,25,45,25,6,7,41,130,130,41,7,8,63,336,650,
%T 336,63,8,9,92,785,2942,2942,785,92,9,10,129,1682,11819,24520,11819,
%U 1682,129,10,11,175,3351,42305,183010,183010,42305,3351,175,11,12,231,6280,136564
%N Array T(n,k) = number of n X k binary matrices with rows and columns in lexicographically nondecreasing order.
%C Differs from "number of inequivalent {0,1}-matrices of size n X k, modulo permutations of rows and columns", A241956, starting at T(2, 3) = 14 while A241956(2, 3) = 13. - _M. F. Hasler_, Apr 27 2022
%H R. H. Hardin, <a href="/A180985/b180985.txt">Table of n, a(n) for n=1..311</a>
%H <a href="/index/Mat#inequiv">Index to OEIS entries related to inequivalent matrices modulo permutation of row and columns</a>.
%F T(n,k) = T(k,n). T(1,k) = k+1. T(2,k) = A004006(k+1). T(3,k) = A184138(k). - _M. F. Hasler_, Apr 27 2022
%e Table starts:
%e ..2...3.....4.......5.........6...........7.............8................9
%e ..3...7....14......25........41..........63............92..............129
%e ..4..14....45.....130.......336.........785..........1682.............3351
%e ..5..25...130.....650......2942.......11819.........42305...........136564
%e ..6..41...336....2942.....24520......183010.......1202234..........6979061
%e ..7..63...785...11819....183010.....2625117......33345183........371484319
%e ..8..92..1682...42305...1202234....33345183.....836488618......18470742266
%e ..9.129..3351..136564...6979061...371484319...18470742266.....818230288201
%e .10.175..6280..402910..36211867..3651371519..358194085968...31887670171373
%e .11.231.11176.1099694.170079565.32017940222.6148026957098.1096628939510047
%e .
%e All solutions for 3 X 3:
%e ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e ..0..0..0....0..0..0....0..0..1....0..0..1....0..0..1....0..1..1....0..0..0
%e ..0..0..1....0..1..1....0..1..0....0..0..1....0..1..1....0..1..1....1..1..1
%e .
%e ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..1....0..0..1
%e ..0..0..1....0..1..1....0..0..1....0..1..1....0..1..1....0..1..0....0..1..0
%e ..1..1..0....1..0..0....1..1..1....1..0..1....1..1..1....0..1..0....0..1..1
%e .
%e ..0..0..1....0..0..1....0..0..1....0..0..1....0..0..1....0..0..1....0..0..1
%e ..0..0..1....0..0..1....0..0..1....0..1..1....0..1..0....0..1..0....0..1..0
%e ..0..1..0....0..0..1....0..1..1....0..1..1....1..0..0....1..1..0....1..0..1
%e .
%e ..0..0..1....0..0..1....0..0..1....0..0..1....0..0..1....0..0..1....0..0..1
%e ..0..1..0....0..0..1....0..1..1....0..1..1....0..0..1....0..1..1....0..1..1
%e ..1..1..1....1..1..0....1..0..0....1..1..0....1..1..1....1..0..1....1..1..1
%e .
%e ..0..0..0....0..0..1....0..0..1....0..0..1....0..1..1....0..1..1....0..1..1
%e ..1..1..1....1..1..0....1..1..0....1..1..1....0..1..1....0..1..1....0..1..1
%e ..1..1..1....1..1..0....1..1..1....1..1..1....0..1..1....1..0..0....1..0..1
%e ...
%e ..0..1..1....0..1..1....0..1..1....0..1..1....0..1..1....0..1..1....0..1..1
%e ..0..1..1....1..0..0....1..0..0....1..0..0....1..0..1....1..0..1....1..0..1
%e ..1..1..1....1..0..0....1..0..1....1..1..1....1..1..0....1..0..1....1..1..1
%e .
%e ..0..1..1....1..1..1
%e ..1..1..1....1..1..1
%e ..1..1..1....1..1..1
%o (PARI) A180985(h,w,cnt=0)={ local(A=matrix(h,w), z(r,c)=!while(r<h, A[r++,c]==A[r,c-1]||return)); while(cnt++, for(r=1,h, for(c=1,w, A[r,c] && next; A[r,c]=1; while(c>1 && z(r,c), c--); while(c>1, A[r,c--]=0); while(r>1, A[r--,]=A[r+1,]); next(3))); break); cnt} \\ _M. F. Hasler_, Apr 27 2022
%Y Cf. A089006 (diagonal).
%Y Cf. A004006 (row & column 2), A184138 (row & column 3).
%Y Cf. A241956 (similar but different).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Sep 30 2010
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