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A302247 Irregular triangle read by rows in which row n lists all parts of all partitions of n, in nondecreasing order. 4
1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..104.

EXAMPLE

Triangle begins:

1;

1,1,2;

1,1,1,1,2,3;

1,1,1,1,1,1,1,2,2,2,3,4;

1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,3,4,5;

1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,4,4,5,6;

...

For n = 4 the partitions of 4 are [4], [2, 2], [3, 1], [2, 1, 1], [1, 1, 1, 1]. There are seven 1's, three 2's, only one 3 and only one 4, so the 4th row of this triangle is [1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 4].

CROSSREFS

Mirror of A302246.

Row n has length A006128(n).

The sum of row n is A066186(n).

The number of parts k in row n is A066633(n,k).

The sum of all parts k in row n is A138785(n,k).

The number of parts >= k in row n is A181187(n,k).

The sum of all parts >= k in row n is A206561(n,k).

The number of parts <= k in row n is A210947(n,k).

The sum of all parts <= k in row n is A210948(n,k).

First differs from both A026791 and A080576 at a(17) = T(4,7).

Sequence in context: A140225 A104758 A143227 * A026791 A080576 A321744

Adjacent sequences:  A302244 A302245 A302246 * A302248 A302249 A302250

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Apr 05 2018

STATUS

approved

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Last modified October 15 09:22 EDT 2019. Contains 328026 sequences. (Running on oeis4.)