A161924 -id:A161924 - cp's OEIS frontend

A167202 Fourth in a series of triangular subarrays of A117506. Previous arrays are Tables A007318, A059797 and A167201.

5, 21, 14, 56, 70, 28, 120, 216, 162, 48

Offset: 1

Alford Arnold, Nov 04 2009

This subarray is generated from values related to the source partition
2+2+2. (cf A161924). Note that A117506(25) maps to Partition 2+2+2
which corresponds to the 14th natural number appearing in A161924.
Note also that Table A167201 is the transpose of Table a(n) and that
partition 3+3 is the conjugate of partition 2+2+2.

			The A161924 domain values begin:
14
22..29
38..45..59
70..77..91..119
so based on function A117506, a(n) begins:
5
21..14
56..70..28
70..77..91..119

A099627 A007318 A124922 A059797 A161924 A167201 A117506

A167204 Triangle read by rows in which row n lists the first 2^(n-1) terms of A003602.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 2, 4, 1, 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16, 1, 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16

Offset: 1

Alford Arnold, Nov 12 2009

The old definition (see history #7) was:

"Numbers such that n is contained in the array a(n) where array 1 is A099627, array 2 is A124922 etc. (Table A167979 illustrates the manner in which the array numbers are chosen - e.g. "12" is not in array 1 or 2 so it begins array 3. All of the arrays can be seen in A161924."

			From _Omar E. Pol_, Feb 21 2011: (Start)
If written as a triangle:
1,
1,1,
1,1,2,1,
1,1,2,1,3,2,4,1,
1,1,2,1,3,2,4,1,5,3,6,2,7,4,8,1,
1,1,2,1,3,2,4,1,5,3,6,2,7,4,8,1,9,5,10,3,11,6,12,2,13,7,14,4,15,8,16,1,
...
(End)
a(12)= 3 therefore, as expected, 12 is contained in array 3; a(14)= 4 so 14 is a member of array 4, etc.
A099627 (array 1) begins 1 2 3 4 5 7 8 9 11 15 ...
A124922 (array 2) begins 6 10 13 18 21 27 ... so a(n) begins 1 1 1 1 1 2 1 1 1 2 1 ...
The next two arrays begin 12 20 25 36 41 51 ... and 14 22 29 38 45 59 ...

Cf. A003602, A099627, A124922, A167201 (uses array 3), A167202 (uses array 4), A161924 (contains all of the arrays), A167979 (Linearizes and concatenates the arrays).

Definition corrected by Alford Arnold, Feb 05 2011
Better definition from Omar E. Pol, Feb 21 2011
Further edits from N. J. A. Sloane, Feb 21 2011
More terms a(64)-a(94) from Omar E. Pol, Feb 22 2011

A167977 Triangle A161511(A167979(n,k)).

Original entry on oeis.org

1, 2, 4, 2, 5, 6, 3, 5, 7, 6, 3, 6, 7, 7, 8, 3, 6, 8, 7, 9, 8, 4, 6, 8, 8, 9, 9, 9, 4, 7, 8, 8, 10, 9, 10, 8, 4, 7, 9, 8, 10, 10, 10, 9, 10

Offset: 1

Alford Arnold, Nov 24 2009

Note that the values of this triangle identify the number partitioned described in A125105 and A161924.

			The triangle A167979 begins
1
2..6
3..10..12
so mapping each value with A161511 generates this triangle here, which begins
1
2..4
2..5..6

Cf. A125106, A161924, A161511, A167979

A173870 Consider each term k contained in A114994; write 2k if and only if 2k is not a member of A114994.

Original entry on oeis.org

6, 14, 20, 22, 30, 38, 46, 62, 70, 72, 78, 84, 86, 94, 126, 134, 142, 148, 150, 158, 174, 190, 254, 262, 270, 272, 276, 278, 286, 294, 302, 318, 340, 342, 350, 382, 510, 518, 526, 532, 534, 542, 550, 558, 574, 584, 590, 596, 598, 606, 638, 686, 702, 766, 1022

Offset: 0

Alford Arnold, Mar 01 2010

Recall that A114994 can be regarded as a table with row lengths A000041(n).
Likewise, a(n) has row lengths 0,1,1,3,3,7,8,14,18,28,35,53,67,... which appears to coincide with sequence A117989.
The row lengths also match 1 2 3 5 7 11 15 22 ... minus 1 1 2 2 4 4 7 8 ... - Alford Arnold, Mar 30 2010

			Row three of A114994 is 4,5,7 when doubled becomes 8,10,14.
8 and 10 are in A114994 so not in a(n); 14 is not in A114994 so is in a(n).

Cf. A000041 A114994 A117989 (A125106, A126441, A161924)(3 closely related sequences).

Cf. A002865 [From Alford Arnold, Mar 30 2010]

cp's OEIS Frontend

A167202 Fourth in a series of triangular subarrays of A117506. Previous arrays are Tables A007318, A059797 and A167201.

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A167204 Triangle read by rows in which row n lists the first 2^(n-1) terms of A003602.

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A167977 Triangle A161511(A167979(n,k)).

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A173870 Consider each term k contained in A114994; write 2k if and only if 2k is not a member of A114994.

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