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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 (list; table; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..82.

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.

Cf. A000041, A008284, A058399, A133041, A135010, A141285, A209656, A207380.

Sequence in context: A209115 A141412 A178623 * A160183 A168534 A026807

Adjacent sequences:  A210762 A210763 A210764 * A210766 A210767 A210768

KEYWORD

nonn,tabl,easy

AUTHOR

Omar E. Pol, Mar 26 2012

STATUS

approved

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Last modified December 8 01:25 EST 2021. Contains 349590 sequences. (Running on oeis4.)