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A249543 Square array T(m,n) of integer partitions with m addends n+1, read by antidiagonals. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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).

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

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.)

CROSSREFS

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

Sequence in context: A060866 A064478 A111798 * A307404 A307405 A115305

Adjacent sequences:  A249540 A249541 A249542 * A249544 A249545 A249546

KEYWORD

nonn,tabl

AUTHOR

Tilman Piesk, Oct 31 2014

STATUS

approved

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Last modified July 23 03:00 EDT 2019. Contains 325230 sequences. (Running on oeis4.)