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A328361 Triangle read by rows: T(n,k) is the total number of k's in all partitions of n into consecutive parts, (1 <= k <= n). 9
1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,40

COMMENTS

Iff n is a power of 2 (A000079) then row n lists n - 1 zeros together with 1.

Iff n is an odd prime (A065091) then row n lists (n - 3)/2 zeros, 1, 1, (n - 3)/2 zeros, 1.

LINKS

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

EXAMPLE

Triangle begins:

1;

0, 1;

1, 1, 1;

0, 0, 0, 1;

0, 1, 1, 0, 1;

1, 1, 1, 0, 0, 1;

0, 0, 1, 1, 0, 0, 1;

0, 0, 0, 0, 0, 0, 0, 1;

0, 1, 1, 2, 1, 0, 0, 0, 1;

1, 1, 1, 1, 0, 0, 0, 0, 0, 1;

0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1;

0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1;

0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1;

0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1;

1, 1, 1, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1;

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

...

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, 1, 1, 2, 1, 0, 0, 0, 1].

CROSSREFS

Row sums give A204217.

Column 1 gives A010054, n >= 1.

Leading diagonal gives A000012.

Cf. A000079, A001227, A065091, A066633, A237048, A237593, A245579, A266531, A285898, A285899, A285900, A285914, A286000, A286001, A299765, A328362.

Sequence in context: A299197 A334196 A143111 * A301367 A334090 A179195

Adjacent sequences:  A328358 A328359 A328360 * A328362 A328363 A328364

KEYWORD

nonn,tabl

AUTHOR

Omar E. Pol, Oct 20 2019

STATUS

approved

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Last modified June 15 15:16 EDT 2021. Contains 345049 sequences. (Running on oeis4.)