

A328362


Triangle read by rows: T(n,k) is the sum of all parts k in all partitions of n into consecutive parts, (1 <= k <= n).


6



1, 0, 2, 1, 2, 3, 0, 0, 0, 4, 0, 2, 3, 0, 5, 1, 2, 3, 0, 0, 6, 0, 0, 3, 4, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 8, 0, 2, 3, 8, 5, 0, 0, 0, 9, 1, 2, 3, 4, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 5, 6, 0, 0, 0, 0, 11, 0, 0, 3, 4, 5, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 6, 7, 0, 0, 0, 0, 0, 13, 0, 2, 3, 4, 5, 0, 0, 0, 0, 0, 0, 0, 0, 14
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OFFSET

1,3


COMMENTS

Iff n is a power of 2 (A000079) then row n lists n  1 zeros together with n.
Iff n is an odd prime (A065091) then row n lists (n  3)/2 zeros, (n  1)/2, (n + 1)/2, (n  3)/2 zeros, n.


LINKS



FORMULA



EXAMPLE

Triangle begins:
1;
0, 2;
1, 2, 3;
0, 0, 0, 4;
0, 2, 3, 0, 5;
1, 2, 3, 0, 0, 6;
0, 0, 3, 4, 0, 0, 7;
0, 0, 0, 0, 0, 0, 0, 8;
0, 2, 3, 8, 5, 0, 0, 0, 9;
1, 2, 3, 4, 0, 0, 0, 0, 0, 10;
0, 0, 0, 0, 5, 6, 0, 0, 0, 0, 11;
0, 0, 3, 4, 5, 0, 0, 0, 0, 0, 0, 12;
0, 0, 0, 0, 0, 6, 7, 0, 0, 0, 0, 0, 13;
0, 2, 3, 4, 5, 0, 0, 0, 0, 0, 0, 0, 0, 14;
1, 2, 3, 8,10, 6, 7, 8, 0, 0, 0, 0, 0, 0, 15;
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16;
...
For n = 9 there are three partitions of 9 into consecutive parts, they are [9], [5, 4], [4, 3, 2], so the 9th row of triangle is [0, 2, 3, 8, 5, 0, 0, 0, 9].


CROSSREFS

Cf. A000079, A001227, A065091, A138785, A204217, A237048, A237593, A266531, A285898, A285899, A285900, A285914, A286000, A286001, A299765, A328361.


KEYWORD



AUTHOR



STATUS

approved



