A340529 Irregular triangle read by rows T(n,k), (n >= 1, k >= 1), in which row n has length A000041(n-1) and every column k is A006218.

1, 3, 5, 1, 8, 3, 1, 10, 5, 3, 1, 1, 14, 8, 5, 3, 3, 1, 1, 16, 10, 8, 5, 5, 3, 3, 1, 1, 1, 1, 20, 14, 10, 8, 8, 5, 5, 3, 3, 3, 3, 1, 1, 1, 1, 23, 16, 14, 10, 10, 8, 8, 5, 5, 5, 5, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 27, 20, 16, 14, 14, 10, 10, 8, 8, 8, 8, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1,2

Links

Table of n, a(n) for n=1..97.

Formula

a(m) = A006218(A336811(m)).

T(n,k) = A006218(A336811(n,k)).

Example

Triangle begins:
   1;
   3;
   5,  1;
   8,  3,  1;
  10,  5,  3,  1,  1;
  14,  8,  5,  3,  3, 1, 1;
  16, 10,  8,  5,  5, 3, 3, 1, 1, 1, 1;
  20, 14, 10,  8,  8, 5, 5, 3, 3, 3, 3, 1, 1, 1, 1;
  23, 16, 14, 10, 10, 8, 8, 5, 5, 5, 5, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1;
...
For n = 6, the length of row 6 is A000041(5) = 7.
The sum of row 6 is 14 + 8 + 5 + 3 + 3 + 1 + 1 = 35, equaling A006128(6).

Crossrefs

Row sums give A006128.

Cf. A340525 (a regular version).

Members of the same family are: A336811, A339278, A339304, A340423.

Cf. A337209, A339258, A340530, A340531.

Cf. A000041, A006218.

Sequence in context: A236631 A302800 A367067 * A197326 A235605 A212695

Adjacent sequences: A340526 A340527 A340528 * A340530 A340531 A340532

Keyword

nonn,tabf

Author

Omar E. Pol, Jan 10 2021

Status

approved