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

1,5

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]

Links

Table of n, a(n) for n=1..60.

J. Stauduhar, Python program

Example

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

Prog

(Python) See Links section.

Crossrefs

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

Sequence in context: A274146 A027189 A140829 * A184324 A274168 A116575

Adjacent sequences: A346520 A346521 A346522 * A346524 A346525 A346526

Keyword

nonn

Author

J. Stauduhar, Jul 21 2021

Extensions

Definition aligned with A028307 by Peter Munn, Nov 20 2021

Status

approved