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A195644
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T(n,k) is the number of lower triangles of an n X n 0..k array with all row sums equal to the length of the row and all column sums equal to the length of the column.
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6
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1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 15, 1, 1, 1, 3, 19, 199, 1, 1, 1, 3, 19, 379, 6247, 1, 1, 1, 3, 19, 391, 22506, 505623, 1, 1, 1, 3, 19, 391, 25428, 4063437, 105997283, 1, 1, 1, 3, 19, 391, 25532, 5422820, 2303397986, 58923059879, 1, 1, 1, 3, 19, 391, 25532, 5536654
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OFFSET
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1,9
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LINKS
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FORMULA
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EXAMPLE
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Table starts:
1 1 1 1 1 1 ...
1 1 1 1 1 1 ...
1 3 3 3 3 3 ...
1 15 19 19 19 19 ...
1 199 379 391 391 391 ...
1 6247 22506 25428 25532 25532 ...
1 505623 4063437 5422820 5536654 5539434 ...
1 105997283 2303397986 3868544673 4102276124 4116036800 ...
...
Some solutions for n=5, k=4:
..1..........1..........1..........1..........1..........1..........1
..1.1........1.1........2.0........2.0........2.0........2.0........2.0
..3.0.0......3.0.0......0.1.2......2.1.0......0.1.2......2.0.1......1.2.0
..0.1.1.2....0.1.1.2....1.1.0.2....0.1.1.2....1.1.0.2....0.0.2.2....1.2.1.0
..0.2.2.0.1..0.2.2.0.1..1.2.1.0.1..0.2.2.0.1..1.2.1.0.1..0.4.0.0.1..0.0.2.2.1
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PROG
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(PARI) \\ adapted from program for A257493.
T(n, k)={
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(h, p, q, v, e) = if(!p, if(!e, acc(q, v)), my(i=poldegree(p), t=pollead(p)); self()(n, p-t*x^i, q+t*x^i, v, e); for(m=1, min(k, h-i), for(j=1, min(t, e\m), self()(if(j==t, n, 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, src[i, 1] + x^(r-1), 0, src[i, 2], r))); vecsum(Mat(M)[, 2])
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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