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 A327913 Array read by antidiagonals: T(n,m) is the number of distinct unordered row and column sums of n X m binary matrices. 3
 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 7, 4, 1, 1, 5, 13, 13, 5, 1, 1, 6, 22, 34, 22, 6, 1, 1, 7, 34, 76, 76, 34, 7, 1, 1, 8, 50, 152, 221, 152, 50, 8, 1, 1, 9, 70, 280, 557, 557, 280, 70, 9, 1, 1, 10, 95, 482, 1264, 1736, 1264, 482, 95, 10, 1, 1, 11, 125, 787, 2630, 4766, 4766, 2630, 787, 125, 11, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Only matrices in which both row and columns sums are weakly increasing need to be considered. If order is also considered then the number of possibilities is given by A328887(n, m). LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1325 Manfred Krause, A simple proof of the Gale-Ryser theorem, American Mathematical Monthly, 1996. Wikipedia, Gale-Ryser theorem EXAMPLE Array begins: ============================================= n\m | 0 1  2   3    4     5     6      7 ----+----------------------------------------   0 | 1 1  1   1    1     1     1      1 ...   1 | 1 2  3   4    5     6     7      8 ...   2 | 1 3  7  13   22    34    50     70 ...   3 | 1 4 13  34   76   152   280    482 ...   4 | 1 5 22  76  221   557  1264   2630 ...   5 | 1 6 34 152  557  1736  4766  11812 ...   6 | 1 7 50 280 1264  4766 15584  45356 ...   7 | 1 8 70 482 2630 11812 45356 153228 ...   ... T(2,2) = 7. The following 7 matrices each have different row/column sums.   [0 0]  [0 0]  [0 1]  [0 0]  [0 1]  [0 1]  [1 1]   [0 0]  [0 1]  [1 0]  [1 1]  [0 1]  [1 1]  [1 1] PROG (PARI) T(n, m)={local(Cache=Map());   my(F(b, c, t, w)=my(hk=Vecsmall([b, c, t, w]), z);      if(!mapisdefined(Cache, hk, &z),        z = if(w&&c, sum(i=0, b, sum(j=ceil((t+i)/w), min(t+i, c), self()(i, j, t+i-j, w-1))), !t);      mapput(Cache, hk, z)); z);    F(n, n, 0, m) } CROSSREFS Main diagonal is A029894. Cf. A028657 (nonequivalent binary n X m matrices). Cf. A318396, A328887. Sequence in context: A094526 A088699 A101515 * A028657 A053534 A104881 Adjacent sequences:  A327910 A327911 A327912 * A327914 A327915 A327916 KEYWORD nonn,tabl AUTHOR Andrew Howroyd, Oct 30 2019 STATUS approved

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Last modified December 9 15:04 EST 2019. Contains 329877 sequences. (Running on oeis4.)