login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A214314 Number triangle with entry T(n,m) giving the position of the first partition of n with m parts in the Abramowitz-Stegun (A-St) partition ordering. 6
1, 1, 2, 1, 2, 3, 1, 2, 4, 5, 1, 2, 4, 6, 7, 1, 2, 5, 8, 10, 11, 1, 2, 5, 9, 12, 14, 15, 1, 2, 6, 11, 16, 19, 21, 22, 1, 2, 6, 13, 19, 24, 27, 29, 30, 1, 2, 7, 15, 24, 31, 36, 39, 41, 42, 1, 2, 7, 17, 28, 38, 45, 50, 53, 55, 56, 1, 2, 8, 20, 35, 48, 59, 66, 71, 74, 76, 77 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

For the Abramowitz-Stegun ordering of partitions see A036036 for the reference and a C. F. Hindenburg link.

The present triangle is the partial sum triangle of the triangle t(n,k) = 0 if 0 <= n -1 <  k , t(n,0) = 1, n >= 1 and t(n,k) = A008284(n,k) if n-1 >=  k >= 1. This triangle with offset [1,0] for [n,k] is 1; 1,1; 1,1,1; 1,1,2,1; 1,1,2,2,1; 1,1,3,3,2,1;... (erase the diagonal of A008284 and add instead a column k=0 with only 1's). See the example section.

LINKS

Table of n, a(n) for n=1..78.

FORMULA

T(n,m) = sum(p(n,k),k=0..m-1) if n >= m >= 1, otherwise 0, with p(n,0) :=1 and p(n,k) = A008284(n,k) for k=1,2,...,n-1.

EXAMPLE

T(n,m) starts with:

n\m   1  2  3   4   5   6   7   8   9  10  11  12...

1     1

2     1  2

3     1  2  3

4     1  2  4   5

5     1  2  4   6   7

6     1  2  5   8  10  11

7     1  2  5   9  12  14  15

8     1  2  6  11  16  19  21  22

9     1  2  6  13  19  24  27  29  30

10    1  2  7  15  24  31  36  39  41  42

11    1  2  7  17  28  38  45  50  53  55  56

12    1  2  8  20  35  48  59  66  71  74  76  77

...

T(6,4) = 8 because the 11=T(6,6) partitions for n=6 are, in A-St order: [6]; [1,5],[2,4],[3,3]; [1^2,4],[1,2,3],[2^3]; [1^3,3],[1^2,2^2]; [1^4,2]; [1^6] and the first partition with 4 parts, appears at position 8.

This triangle is obtained as partial sum triangle from the triangle t(n,k) (see the comment section) which starts with:

n\m   0  1  2   3   4   5   6  7  8  9 10 11 ...

1     1

2     1  1

3     1  1  1

4     1  1  2   1

5     1  1  2   2   1

6     1  1  3   3   2   1

7     1  1  3   4   3   2   1

8     1  1  4   5   5   3   2  1

9     1  1  4   7   6   5   3  2  1

10    1  1  5   8   9   7   5  3  2  1

11    1  1  5  10  11  10   7  5  3  2  1

12    1  1  6  12  15  13  11  7  5  3  2  1

...

CROSSREFS

Cf. A008284.

Sequence in context: A104795 A116925 A210950 * A209435 A263744 A268956

Adjacent sequences:  A214311 A214312 A214313 * A214315 A214316 A214317

KEYWORD

nonn,tabl

AUTHOR

Wolfdieter Lang, Jul 24 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 15 21:01 EST 2018. Contains 318154 sequences. (Running on oeis4.)