A122402 -id:A122402 - cp's OEIS frontend

A122453 Triangular array related to A122402 as A079025 relates to A122172; sums A079139 values associated with cyclic partitions.

1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 3, 2, 2, 3, 4, 4, 3, 2, 4, 8, 13, 15, 13, 8, 4, 4, 8, 13, 16, 16, 13, 8, 4, 7, 17, 32, 45, 51, 45, 32, 17, 7, 8, 20, 38, 56, 67, 67, 56, 38, 20, 8, 12, 34, 72, 117, 156, 171, 156, 117, 72, 34, 12, 14, 41, 88, 147, 203, 237, 237, 203, 147, 88, 41

Offset: 0

Alford Arnold, Sep 07 2006

			The table begins:
1
0 0
1 1 1
1 1 1 1
2 3 4 3 2
2 3 4 4 3 2
4 8 13 15 13 8 4
4 8 13 16 16 13 8 4
7 17 32 45 51 45 32 17 7
8 20 38 56 67 67 56 38 20 8
12 34 72 117 156 171 156 117 72 34 12
14 41 88 147 203 237 237 203 147 88 41 14

Cf. A002865 A074139 A079025 A122172 A122402.

A122401 Subsequence of A074139 omitting values derived from partitions with a part of size 1.

Original entry on oeis.org

1, 3, 4, 5, 9, 6, 12, 7, 15, 16, 27, 8, 18, 20, 36, 9, 21, 24, 25, 45, 48, 81, 10, 24, 28, 30, 54, 60, 64, 108, 11, 27, 32, 35, 63, 36, 72, 75, 80, 135, 144, 243, 12, 30, 36, 40, 72, 42, 84, 90, 96, 162, 100, 180, 192, 324, 13, 33, 40, 45, 81, 48, 96, 49, 105, 112, 189, 108, 120, 216, 125, 225, 240, 405, 256, 432, 729, 14, 36, 44, 50, 90, 54

Offset: 0

Alford Arnold, Sep 01 2006

When viewed as a table, row sums are given by sequence A079274.

Corresponds to members of A036035 which are also powerful numbers (A001694).

			The two cyclic partitions of five are 5 and 3+2 yielding (5+1)=6 and (3+1)*(2+1) = 4*3 = 12
The array begins
1
(empty)
3
4
5 9
6 12
7 15 16 27
8 18 20 36

Cf. A122172 A079274 A122402, A316532.

A122401_row := proc(n)
    local e, a,L;
    L := [] ;
    for e in ListTools[Reverse](partition(n)) do
        if member(1,e) then
            ;
        else
            a := 1;
            for p in e do
                a := a*(p+1) ;
            end do:
            L := [op(L),a] ;
        end if;
    end do:
    L ;
end proc:
seq(A122401_row(i), i=0..15); # R. J. Mathar, Aug 28 2018

Extended by R. J. Mathar, Aug 28 2018

A122403 Table read by rows: rearrangement of A122401 to illustrate linear column sequences.

Original entry on oeis.org

1, 0, 3, 4, 5, 9, 6, 12, 7, 15, 16, 27, 8, 18, 20, 36, 9, 21, 24, 45, 25, 48, 81, 10, 24, 28, 54, 30, 60, 108, 64, 11, 27, 32, 63, 35, 72, 135, 80, 36, 75, 144, 243, 12, 30, 36, 72, 40, 84, 162, 96, 42, 90, 180, 324, 100, 192

Offset: 0

Alford Arnold, Sep 03 2006

			The row sums and array begin:
1 1
0 0
3 3
4 4
14 5 9
18 6 12
65 7 15 16 27
82 8 18 20 36
253 9 21 24 45 25 48 81
378 10 24 28 54 30 60 108 64
953 11 27 32 63 35 72 135 80 36 75 144 243
1460 12 30 36 72 40 84 162 96 42 90 180 324 100 192

Cf. A122172 A122401 A122402.

cp's OEIS Frontend

A122453 Triangular array related to A122402 as A079025 relates to A122172; sums A079139 values associated with cyclic partitions.

Views

Author

Keywords

Examples

Crossrefs

A122401 Subsequence of A074139 omitting values derived from partitions with a part of size 1.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

Extensions

A122403 Table read by rows: rearrangement of A122401 to illustrate linear column sequences.

Views

Author

Keywords

Examples

Crossrefs