The On-Line Encyclopedia of Integer Sequences (OEIS)

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A330369

Triangle read by rows: T(n,k) (1 <= k <= n) is the total number of right angles of size k in all partitions of n.
(history; published version)

#59 by N. J. A. Sloane at Fri Nov 20 21:16:31 EST 2020

STATUS

editing

approved

#58 by N. J. A. Sloane at Fri Nov 20 21:15:35 EST 2020

AUTHOR

Omar E. Pol, Dec 12 2019.

Discussion

Fri Nov 20

21:16

N. J. A. Sloane: Sorry, you had the correct spelling, Ferrers.

#57 by N. J. A. Sloane at Fri Nov 20 21:14:02 EST 2020

NAME

Triangle read by rows: T(n,k) (1 <= k <= n) is the total number of right angles of size k of in all partitions of n, with 1 <= k <= n.

COMMENTS

This triangle has the property that it contains too the triangle A049597, since if we replace with zeros the positive terms before the first zero in the row n of this triangle, so we have get the triangle A049597.

REFERENCES

G. E. Andrews, Theory of Partitions, Cambridge University Press, 1984, page 143 [Defines the right angles in the Ferrers graph of a partition. - _N. J. A. Sloane_, Nov 20 2020]

EXAMPLE

...

Below the figure Figure 1 below shows the Ferrers diagram of the partition of 24: [7, 6, 3, 3, 2, 1, 1, 1]. The figure Figure 2 shows the right-angles diagram of the same partition. Note that in this last diagram we can see the size of the three right angles as follows: the first right angle has size 14 because it contains 14 square cells, the second right angle has size 8 and the third right angle has size 2.

For n = 8 the partitions of 8 and their respective right-angles diagrams look like are as shown belowfollows:

STATUS

proposed

editing

Discussion

Fri Nov 20

21:14

N. J. A. Sloane: Many edits. Ferrers, not Ferrars.

#56 by Omar E. Pol at Fri Nov 13 18:02:43 EST 2020

STATUS

editing

proposed

#55 by Omar E. Pol at Fri Nov 13 18:02:37 EST 2020

NAME

Triangle read by rows: T(n,k) is the total number of right angles of size k of all partitions of n, with 1 <= k <= n.

STATUS

proposed

editing

#54 by Omar E. Pol at Fri Nov 13 13:12:48 EST 2020

STATUS

editing

proposed

#53 by Omar E. Pol at Fri Nov 13 13:12:42 EST 2020

CROSSREFS

Cf. A000041, A049597, A083480, A083906, A188674, A259481, A325458, A330375, A330378, A330379.

STATUS

proposed

editing

#52 by Omar E. Pol at Fri Nov 13 13:06:50 EST 2020

STATUS

editing

proposed

#51 by Omar E. Pol at Fri Nov 13 13:06:42 EST 2020

CROSSREFS

Cf. A000041, A049597, A083480, A083906, A188674, A259481, A325458, A330375, A330379.

STATUS

proposed

editing

#50 by Omar E. Pol at Fri Nov 13 13:05:31 EST 2020

STATUS

editing

proposed