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A194549 Triangle read by rows: T(n,k) = Dyson's rank of the k-th partition of n that does not contain 1 as a part, with partitions in lexicographic order. 7
1, 1, 2, 0, 3, 1, 4, -1, 2, 1, 5, 0, 3, 2, 6, -2, 1, 0, 4, 3, 2, 7, -1, 2, 1, 5, 0, 4, 3, 8, -3, 0, -1, 3, 2, 1, 6, 1, 5, 4, 3, 9, -2, 1, 0, 4, -1, 3, 2, 7, 2, 1, 6, 5, 4, 10, -4, -1, -2, 2, 1, 0, 5, 0, 4, 3, 2, 8, -1, 3, 2, 7, 1, 6, 5, 4, 11, -3, 0, -1, 3, -2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Rows n = 1..33, flattened

FORMULA

a(n) = A141285(n) - A194548(n).

EXAMPLE

Written as a triangle:

1;

1;

2;

0,3;

1,4;

-1,2,1,5;

0,3,2,6;

-2,1,0,4,3,2,7;

-1,2,1,5,0,4,3,8;

-3,0,-1,3,2,1,6,1,5,4,3,9;

-2,1,0,4,-1,3,2,7,2,1,6,5,4,10;

-4,-1,-2,2,1,0,5,0,4,3,2,8,-1,3,2,7,1,6,5,4,11;

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;

      if n<2 then 1 else l:= NULL; b(n, 2, 0); l fi

    end:

seq(T(n), n=1..13); # Alois P. Heinz, Dec 20 2011

CROSSREFS

The sum of row n is A000041(n-1). Row n has length A187219(n).

Cf. A002865, A135010, A138121, A194546, A194547, A194548.

Sequence in context: A135156 A277707 A316524 * A063277 A029178 A082375

Adjacent sequences:  A194546 A194547 A194548 * A194550 A194551 A194552

KEYWORD

sign,tabf,look

AUTHOR

Omar E. Pol, Dec 11 2011

EXTENSIONS

More terms from Alois P. Heinz, Dec 20 2011

STATUS

approved

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Last modified October 19 21:07 EDT 2019. Contains 328227 sequences. (Running on oeis4.)