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A194547
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Triangle read by rows: T(n,k) = Dyson's rank of the k-th partition of n, with partitions in lexicographic order.
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9
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0, -1, 1, -2, 0, 2, -3, -1, 1, 0, 3, -4, -2, 0, -1, 2, 1, 4, -5, -3, -1, -2, 1, 0, 3, -1, 2, 1, 5, -6, -4, -2, -3, 0, -1, 2, -2, 1, 0, 4, 0, 3, 2, 6, -7, -5, -3, -4, -1, -2, 1, -3, 0, -1, 3, -1, 2, 1, 5, -2, 1, 0, 4, 3, 2, 7, -8, -6, -4, -5, -2, -3, 0, -4, -1
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OFFSET
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1,4
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COMMENTS
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Row n has length A000041(n). The sum of row n is equal to zero.
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LINKS
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FORMULA
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EXAMPLE
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Written as a triangle:
0;
-1,1;
-2,0,2;
-3,-1,1,0,3;
-4,-2,0,-1,2,1,4;
-5,-3,-1,-2,1,0,3,-1,2,1,5;
-6,-4,-2,-3,0,-1,2,-2,1,0,4,0,3,2,6;
-7,-5,-3,-4,-1,-2,1,-3,0,-1,3,-1,2,1,5,-2,1,0,4,3,2,7;
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MAPLE
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T:= proc(n) local b, l;
b:= proc(n, i, t)
if n=0 then l:=l, i-t
elif i>n then
else b(n-i, i, t+1); b(n, i+1, t)
fi
end;
l:= NULL; b(n, 1, 0); l
end:
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MATHEMATICA
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T[n_] := Module[{b, l}, b[n0_, i_, t_] := If [n0==0, l = Append[l, i-t], If[i>n0, , b[n0-i, i, t+1]; b[n0, i+1, t]]]; l = {}; b[n, 1, 0]; l];
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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