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A340525 Triangle read by rows: T(n,k) = A006218(n-k+1)*A002865(k-1), 1 <= k <= n. 3
1, 3, 0, 5, 0, 1, 8, 0, 3, 1, 10, 0, 5, 3, 2, 14, 0, 8, 5, 6, 2, 16, 0, 10, 8, 10, 6, 4, 20, 0, 14, 10, 16, 10, 12, 4, 23, 0, 16, 14, 20, 16, 20, 12, 7, 27, 0, 20, 16, 28, 20, 32, 20, 21, 8, 29, 0, 23, 20, 32, 28, 40, 32, 35, 24, 12, 35, 0, 27, 23, 40, 32, 56, 40, 56, 40, 36, 14 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjecture: the sum of row n equals A006128(n), the total number of parts in all partitions of n.

LINKS

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

EXAMPLE

Triangle begins:

   1;

   3,  0;

   5,  0,  1;

   8,  0,  3,  1;

  10,  0,  5,  3,  2;

  14,  0,  8,  5,  6,  2;

  16,  0, 10,  8, 10,  6,  4;

  20,  0, 14, 10, 16, 10, 12,  4;

  23,  0, 16, 14, 20, 16, 20, 12,  7;

  27,  0, 20, 16, 28, 20, 32, 20, 21,  8;

  29,  0, 23, 20, 32, 28, 40, 32, 35, 24, 12;

  35,  0, 27, 23, 40, 32, 56, 40, 56, 40, 36, 14;

...

For n = 6 the calculation of every term of row 6 is as follows:

--------------------------

k   A002865         T(6,k)

--------------------------

1      1   *  14   =  14

2      0   *  10   =   0

3      1   *   8   =   8

4      1   *   5   =   5

5      2   *   3   =   6

6      2   *   1   =   2

.           A006218

--------------------------

The sum of row 6 is 14 + 0 + 8 + 5 + 6 + 2 = 35, equaling A006128(6).

CROSSREFS

Mirror of A245095.

Row sums give A006128 (conjectured).

Columns 1, 3 and 4 are A006218.

Column 2 gives A000004.

Leading diagonal gives A002865.

Cf. A135010, A138121, A221531, A336811, A339106, A340424, A340524, A340426.

Sequence in context: A276833 A166586 A122274 * A003966 A123931 A058026

Adjacent sequences:  A340522 A340523 A340524 * A340526 A340527 A340528

KEYWORD

nonn,tabl

AUTHOR

Omar E. Pol, Jan 10 2021

STATUS

approved

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Last modified May 17 12:55 EDT 2021. Contains 343971 sequences. (Running on oeis4.)