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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 (list; table; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..105.

FORMULA

T(n,k) = k*A328361(n,k).

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

Row sums give A245579.

Column 1 gives A010054, n => 1.

Leading diagonal gives A000027.

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

Sequence in context: A138262 A276990 A127510 * A158810 A129391 A129390

Adjacent sequences:  A328359 A328360 A328361 * A328363 A328364 A328365

KEYWORD

nonn,tabl

AUTHOR

Omar E. Pol, Oct 20 2019

STATUS

approved

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Last modified July 23 21:46 EDT 2021. Contains 346265 sequences. (Running on oeis4.)