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A339884 Triangle read by rows: T(n, m) gives the number of partitions of n with m parts and parts from {1, 2, 3}. 0
1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 0, 1, 2, 1, 1, 0, 1, 2, 2, 1, 1, 0, 0, 2, 2, 2, 1, 1, 0, 0, 1, 3, 2, 2, 1, 1, 0, 0, 1, 2, 3, 2, 2, 1, 1, 0, 0, 0, 2, 3, 3, 2, 2, 1, 1, 0, 0, 0, 1, 3, 3, 3, 2, 2, 1, 1, 0, 0, 0, 1, 2, 4, 3, 3, 2, 2, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

Row sums give A001399(n), for n >= 1.

One could add the column [1,repeat 0] for m = 0 starting with n >= 0.

LINKS

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

FORMULA

Sum_{k=0..n} (-1)^k * T(n,k) = A291983(n). - Alois P. Heinz, Feb 01 2021

EXAMPLE

The triangle T(n,m) begins:

n\m  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...

1:   1

2:   1 1

3:   1 1 1

4:   0 2 1 1

5:   0 1 2 1 1

6:   0 1 2 2 1 1

7:   0 0 2 2 2 1 1

8:   0 0 1 3 2 2 1 1

9:   0 0 1 2 3 2 2 1 1

10:  0 0 0 2 3 3 2 2 1  1

11:  0 0 0 1 3 3 3 2 2  1  1

12:  0 0 0 1 2 4 3 3 2  2  1  1

13:  0 0 0 0 2 3 4 3 3  2  2  1  1

14:  0 0 0 0 1 3 4 4 3  3  2  2  1  1

15:  0 0 0 0 1 2 4 4 4  3  3  2  2  1  1

16:  0 0 0 0 0 2 3 5 4  4  3  3  2  2  1  1

17:  0 0 0 0 0 1 3 4 5  4  4  3  3  2  2  1  1

18:  0 0 0 0 0 1 2 4 5  5  4  4  3  3  2  2  1  1

19:  0 0 0 0 0 0 2 3 5  5  5  4  4  3  3  2  2  1  1

20:  0 0 0 0 0 0 1 3 4  6  5  5  4  4  3  3  2  2  1  1

...

Row n = 6: the partitions of 6 with number of parts m = 1,2, ...., 6, and parts from {1,2,3} are (in Abramowitz-Stegun order): [] | [],[],[3,3] | [],[1,2,3],[2^3] | [1^3,3],[1^2,2^2] | [1^4,2] | 1^6, giving 0, 1, 2, 2, 1, 1.

CROSSREFS

Cf. A001399, A008284 (all parts), A145362 (parts 1, 2), A291983.

Compositions: A007818, A030528 (parts 1, 2), A078803 (parts 1, 2, 3).

Sequence in context: A300185 A262804 A048825 * A116375 A301343 A054078

Adjacent sequences:  A339881 A339882 A339883 * A339885 A339887 A339888

KEYWORD

nonn,tabl,easy

AUTHOR

Wolfdieter Lang, Jan 31 2021

STATUS

approved

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Last modified April 15 07:59 EDT 2021. Contains 342975 sequences. (Running on oeis4.)