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A086753
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Number of distinct entries in a slice of A046816.
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2
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1, 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 16, 19, 21, 24, 25, 30, 32, 37, 40, 43, 46, 51, 56, 59, 64, 67, 75, 79, 83, 91, 93, 102, 108, 111, 119, 125, 131, 139, 147, 154, 160, 167, 175, 183, 189, 199, 206, 214, 225, 233, 243, 250, 261, 268, 279, 289, 298, 309, 317
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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LINKS
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EXAMPLE
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The slice for n=4 is
1
4 4
6 12 6
4 12 12 4
1 4 6 4 1
with distinct entries 1,4,6,12, so a(4) = 4.
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MAPLE
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p:= proc(i, j, k) option remember;
if i<0 or j<0 or k<0 or i>k or j>i then 0
elif {i, j, k}={0} then 1
else p(i, j, k-1) +p(i-1, j, k-1) +p(i-1, j-1, k-1)
fi
end:
a:= n-> nops({seq(seq(p(i, j, n), j=0..i), i=0..n)}):
#
#
seq(nops({seq(seq(n!/(i!*j!*(n-i-j)!), j=i..(n-i)/2), i=0..n/3)}), n=0..100); # Robert Israel, Jul 02 2015
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MATHEMATICA
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Table[Length @ Union @ Flatten @ Table[Table[n!/(i!*j!*(n-i-j)!), {j, i, (n-i)/2}], {i, 0, n/3}], {n, 0, 100}] (* Jean-François Alcover, Mar 19 2019, after Robert Israel *)
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PROG
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(PARI) { pt=vector(40, i, matrix(i, i)); pt[1][1, 1]=1; pt[2][1, 1]=1; pt[2][2, 1]=1; pt[2][2, 2]=1; pt[3][1, 1]=1; pt[3][2, 1]=2; pt[3][2, 2]=2; pt[3][3, 1]=1; pt[3][3, 2]=2; pt[3][3, 3]=1; for (i=4, 40, for (j=2, i-1, pt[i][j, 1]=pt[i-1][j-1, 1]+pt[i-1][j, 1]; pt[i][j, j]=pt[i][j, 1]; pt[i][i, j]=pt[i][j, 1] ); pt[i][1, 1]=1; pt[i][i, 1]=1; pt[i][i, i]=1; for(j=3, i-1, for (k=2, j-1, pt[i][j, k]=pt[i-1][j, k]+pt[i-1][j-1, k]+pt[i-1][j-1, k-1]))); pt } { makept(x)=local(xl, v, vc, uc); xl=length(x); v=vector(xl*(xl+1)/2); vc=0; for (i=1, xl, for (j=1, i, v[vc++ ]=x[i, j])); v=vecsort(v); uc=1; for (i=2, length(v), if (v[i]!=v[i-1], uc++)); print1(", "uc) } for (i=1, 40, makept(pt([i]))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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