A123682 -id:A123682 - cp's OEIS frontend

A124222 Triangular array read by rows, with shape sequence A002865, generated from A123682.

1, 1, 3, 5, 0, 9, 2, 13, 7, 1, 0, 19, 18, 4, 2, 25, 36, 12, 10, 0, 2, 0, 33, 64, 26, 32, 2, 11, 2, 1, 41, 103, 49, 78, 7, 40, 13, 6, 1, 0, 3, 0

Offset: 1

Alford Arnold, Oct 19 2006

The shape sequence for A124222 is essentially A002865 since its columns are based on source partitions (1,22,33,222,44,332,2222,333,...). The row sum sequence for A124222 is essentially A001045.

			The array begins
1
1
3
5 0
9 2
13 7 1 0
19 18 4 2
25 36 12 10 0 2 0
33 64 26 32 2 11 2 1
41 103 49 78 7 40 13 6 1 0 3 0

Cf. A001045 (row sums), A002865, A099392, A123682, A123683.

A123683 Second in an infinite series of triangular arrays which, when taken together, sum to 1,1,3,5,11,21,43,85,..., cf. A001045.

Original entry on oeis.org

0, 1, 1, 0, 4, 3, 1, 2, 9, 6, 0, 4, 6, 16, 10, 1, 2, 9, 12, 25, 15, 0, 4, 6, 16, 20, 36, 21, 1, 2, 9, 12, 25, 30, 49, 28

Offset: 1

Alford Arnold, Oct 06 2006, Oct 19 2006

The starting row for each triangle is determined by the applicable source integer partition; thus for partitions 1,22,33,222,44,332,2222,333,... the starting rows are 1,4,6,6,8,8,8,9,...

			Summing the row sums of the triangular arrays we have
1 1
1 1
3 3
5 5 0
11 9 2
21 13 7 1 0
43 19 18 4 2
85 25 36 12 10 2
...

Cf. A000041 A059841 A000217 A000290 A001045 A123640 A123682.

Cf. A000035 A002378.

cp's OEIS Frontend

A124222 Triangular array read by rows, with shape sequence A002865, generated from A123682.

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