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A194547 Triangle read by rows: T(n,k) = Dyson's rank of the k-th partition of n, with partitions in lexicographic order. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Row n has length A000041(n). The sum of row n is equal to zero.

LINKS

Alois P. Heinz, Rows n = 1..26, flattened

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

CROSSREFS

Cf. A105805, A135010, A138121, A194546, A194548, A194549.

Sequence in context: A089596 A319876 A105805 * A257570 A220417 A049581

Adjacent sequences:  A194544 A194545 A194546 * A194548 A194549 A194550

KEYWORD

sign,tabf,look

AUTHOR

Omar E. Pol, Dec 10 2011

EXTENSIONS

More terms from Alois P. Heinz, Dec 22 2011

STATUS

approved

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Last modified October 20 22:37 EDT 2019. Contains 328291 sequences. (Running on oeis4.)