login
A188139
Triangle by rows, A027293 * A129372 as infinite lower triangular matrices
0
1, 1, 1, 3, 1, 1, 4, 2, 1, 1, 8, 3, 2, 1, 1, 11, 6, 3, 2, 1, 1, 19, 8, 5, 3, 2, 1, 1, 26, 13, 7, 5, 3, 2, 1, 1, 41, 18, 12, 7, 5, 3, 2, 1, 1, 56, 28, 16, 11, 7, 5, 3, 2, 1, 1, 83, 38, 24, 15, 11, 7, 5, 3, 2, 1, 1, 112, 55, 33, 23, 15, 11, 7, 5, 3, 2, 1, 1
OFFSET
1,4
COMMENTS
Row sums = A066897: (1, 2, 5, 8, 15, 24, 39,...), total number of odd parts in all partitions of n.
Apparently T(n,k) is the number of (2*k)'s in all the partitions of (n+k), k>=1, e.g. T(7,3) = number of 6's in partitions of 10 = A024790(10). [David Scambler, May 24 2012]
EXAMPLE
First few rows of the triangle =
.
1,
1, 1
3, 1, 1
4, 2, 1, 1
8, 3, 2, 1, 1
11, 6, 3, 2, 1, 1
19, 8, 5, 3, 2, 1, 1
26, 13, 7, 5, 3, 2, 1, 1
41, 18, 12, 7, 5, 3, 2, 1, 1
56, 28, 16, 11, 7, 5, 3, 2, 1, 1
83, 38, 24, 15, 11, 7, 5, 3, 2, 1, 1
112, 55, 33, 23, 15, 11, 7, 5, 3, 2, 1, 1
160, 74, 47, 31, 22, 15, 11, 7, 5, 3, 2, 1, 1,
...
MATHEMATICA
Table[Count[Flatten[IntegerPartitions[n+k]], 2*k], {n, 1, 15}, {k, 1, n}] (* David Scambler, May 24 2012 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Mar 21 2011
EXTENSIONS
a(22) ff. corrected and more terms from Georg Fischer, Jun 10 2023
STATUS
approved