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A346523
Number of sum pyramids for n.
3
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]
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
KEYWORD
nonn
AUTHOR
J. Stauduhar, Jul 21 2021
EXTENSIONS
Definition aligned with A028307 by Peter Munn, Nov 20 2021
STATUS
approved