A346523 Number of sum pyramids for n.

1, 1, 1, 1, 2, 2, 3, 3, 5, 5, 7, 9, 11, 11, 18, 17, 22, 23, 29, 31, 38, 37, 46, 49, 58, 59, 72, 76, 86, 90, 106, 115, 131, 140, 159, 177, 189, 204, 236, 254, 274, 292, 328, 355, 398, 404, 455, 485, 518, 555, 622, 647, 698, 727, 808, 837, 922, 939, 1032, 1100

Offset: 1

Author

J. Stauduhar, Jul 21 2021

Keywords

• nonn

Comments

A sum pyramid for n is defined to be a pyramid with n at its apex, all pairs of adjacent members (x, y) of rows 2,3,4,... sum to the element immediately above, every element is positive and distinct, rows are complete (length of row m = length of row (m-1) + 1), reflections are not counted, and the pyramid is maximal (i.e., not part of a larger pyramid that qualifies). An example of the meaning of "maximal" can be seen in the Example section: the pyramids

.

9 9

6 3 and 5 4

.

are not counted because they consist of the top 2 rows of larger (3-row) pyramids that are counted. [Clarified by Peter Munn, Nov 20 2021]

Examples

			The five pyramids for a(9) are:
                9       9       9
   9     9     6 3     6 3     5 4
  8 1   7 2   5 1 2   4 2 1   2 3 1
		

Links

• J. Stauduhar, Python program

Crossrefs

Cf. A028307 (record pyramid heights), A337766, A348850.

Programs

Python

See Links section.

Extensions

Definition aligned with A028307 by Peter Munn, Nov 20 2021