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A210765
Triangle read by rows in which row n lists the number of partitions of n together with n-1 ones.
2
1, 2, 1, 3, 1, 1, 5, 1, 1, 1, 7, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 22, 1, 1, 1, 1, 1, 1, 1, 30, 1, 1, 1, 1, 1, 1, 1, 1, 42, 1, 1, 1, 1, 1, 1, 1, 1, 1, 56, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 77, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 101, 1, 1, 1
OFFSET
1,2
COMMENTS
The sum of row n is S_n = n - 1 + A000041(n) = A133041(n) - 1.
Also consider a vertical rectangle on the infinite square grid with shorter side = n and longer side = p(n) = A000041(n). Each row of rectangle represents a partition of n. Each part of each partition of n is a horizontal rectangle with shorter side = 1 and longer side = k, where k is the size of the part. It appears that T(n,k) is also the number of k-th parts of all partitions of n in the k-th column of rectangle.
EXAMPLE
Triangle begins:
1;
2, 1;
3, 1, 1;
5, 1, 1, 1;
7, 1, 1, 1, 1;
11, 1, 1, 1, 1, 1;
15, 1, 1, 1, 1, 1, 1;
22, 1, 1, 1, 1, 1, 1, 1;
30, 1, 1, 1, 1, 1, 1, 1, 1;
42, 1, 1, 1, 1, 1, 1, 1, 1, 1;
CROSSREFS
Main diagonal of A209655 and of A209918.
Sequence in context: A353391 A141412 A178623 * A362372 A160183 A168534
KEYWORD
nonn,tabl,easy
AUTHOR
Omar E. Pol, Mar 26 2012
STATUS
approved