A188403 T(n,k) = Number of (n*k) X k binary arrays with rows in nonincreasing order, n ones in every column and no more than 2 ones in any row.
1, 2, 1, 4, 3, 1, 10, 11, 4, 1, 26, 56, 23, 5, 1, 76, 348, 214, 42, 6, 1, 232, 2578, 2698, 641, 69, 7, 1, 764, 22054, 44288, 14751, 1620, 106, 8, 1, 2620, 213798, 902962, 478711, 62781, 3616, 154, 9, 1, 9496, 2313638, 22262244, 20758650, 3710272, 222190, 7340, 215, 10, 1
Offset: 1
Examples
Table starts 1 2 4 10 26 76 232 764 2620 1 3 11 56 348 2578 22054 213798 2313638 1 4 23 214 2698 44288 902962 22262244 648446612 1 5 42 641 14751 478711 20758650 1158207312 80758709676 1 6 69 1620 62781 3710272 313568636 36218801244 5518184697792 1 7 106 3616 222190 22393101 3444274966 767013376954 ... 1 8 154 7340 681460 111200600 29445929253 ... 1 9 215 13825 1865715 472211360 ... 1 10 290 24510 4655535 ... 1 11 381 41336 ... ... All solutions for 4 X 2: ..1..0....1..1....1..1 ..1..0....1..1....1..0 ..0..1....0..0....0..1 ..0..1....0..0....0..0
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..351 (first 95 terms from R. H. Hardin; terms 96..153 from Alois P. Heinz)
- J.-C. Novelli, J.-Y. Thibon, Hopf Algebras of m-permutations,(m+1)-ary trees, and m-parking functions, arXiv preprint arXiv:1403.5962, 2014
Crossrefs
Programs
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PARI
T(k,n)={ local(M=Map(Mat([0, 1]))); my(acc(p, v)=my(z); mapput(M, p, if(mapisdefined(M, p, &z), z+v, v))); my(recurse(r, h, p, q, v, e) = if(!p, acc(x^e+q, v), my(i=poldegree(p), t=pollead(p)); self()(r, k, p-t*x^i, q+t*x^i, v, e); for(m=1, h-i, for(j=1, min(t, (k-e)\m), self()(r, if(j==t, k, i+m-1), p-j*x^i, q+j*x^(i+m), binomial(t, j)*v, e+j*m))))); for(r=1, n, my(src=Mat(M)); M=Map(); for(i=1, matsize(src)[1], recurse(n-r, k, src[i, 1], 0, src[i, 2], 0))); vecsum(Mat(M)[,2]); } {for(n=1, 7, for(k=1, 7, print1(T(n,k),", ")); print)} \\ Andrew Howroyd, Apr 08 2020
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