login
A194547
Triangle read by rows: T(n,k) = Dyson's rank of the k-th partition of n, with partitions in lexicographic order.
9
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
OFFSET
1,4
COMMENTS
Row n has length A000041(n). The sum of row n is equal to zero.
LINKS
FORMULA
a(n) = A194546(n) - A193173(n).
EXAMPLE
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;
MAPLE
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:
seq(T(n), n=1..10); # Alois P. Heinz, Dec 22 2011
MATHEMATICA
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];
Table[T[n], {n, 1, 10}] // Flatten (* Jean-François Alcover, Mar 05 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
sign,tabf,look
AUTHOR
Omar E. Pol, Dec 10 2011
EXTENSIONS
More terms from Alois P. Heinz, Dec 22 2011
STATUS
approved