A249543 Square array T(m,n) of integer partitions with m addends n+1, read by antidiagonals.

1, 2, 3, 4, 9, 7, 6, 20, 26, 15, 10, 40, 72, 68, 30, 14, 75, 171, 220, 159, 56, 21, 133, 379, 614, 603, 352, 101, 29, 229, 786, 1559, 1928, 1525, 732, 176, 41, 383, 1568, 3700, 5564, 5534, 3618, 1465, 297

Offset

1,2

Comments

T(m,n) is the integer partition with m times the addend n+1 (and no other non-one addends) given as index number of A194602.

The entries in the array A249544 are also in the sequence A194602. This array T contains the index numbers of A194602 corresponding to the entries of that array: A194602(T(m,n)) = A249544(m,n).

Row 1 is A000065, column 1 is A058695 (both with shifted index).

Links

Tilman Piesk, First 113 rows of the triangle, flattened

Tilman Piesk, Table for A194602

Li-yao Xia, Identities for A194602

Formula

A194602(T(m,n)) = A249544(m,n).

T(1,n) = A000065(n+1) = p(n+1) - 1.

T(2,n) = p(2*(n+1)) - 2.

T(3,n) = p(3*(n+1)) - floor((n+1)/2) - 3.

T(m,1) = A058695(m-1) = p(2n-1).

p is the sequence of partition numbers A000041. (See "Identities for A194602" link.)

Example

T(5,2) = 159.
A194602(159) = 14043. (So A249544(5,2) = 14043.)
14043 in binary is 11011011011011. That corresponds to the integer partition with 5 times the addend 3. (See row 159 in "Table for A194602" link.)
Array begins:
   n    1    2    3    4    5    6    7   8   9
m
1       1    2    4    6   10   14   21  29  41
2       3    9   20   40   75  133  229 383
3       7   26   72  171  379  786 1568
4      15   68  220  614 1559 3700
5      30  159  603 1928 5564
6      56  352 1525 5534
7     101  732 3618
8     176 1465
9     297

Crossrefs

Cf. A194602, A249544, A000065, A058695, A000041.

Sequence in context: A064478 A111798 A375015 * A307404 A307405 A115305

Adjacent sequences: A249540 A249541 A249542 * A249544 A249545 A249546

Keyword

nonn,tabl

Author

Tilman Piesk, Oct 31 2014

Status

approved