A365081 Numbers k with the property that the symmetric representation of sigma(k) has four parts and its second part is an octagon of width 1 and one of the vertices of the octagon is also the central vertex of the first valley of the largest Dyck path of the diagram.

21, 27, 33, 39, 51, 57, 69, 87, 93, 111, 123, 129, 141, 159, 177, 183, 201, 213, 219, 237, 249, 267, 291, 303, 309, 321, 327, 339, 381

Offset

1,1

Comments

Also the row numbers of the triangle A364639 where the rows are [0, 0, 1, 0, -1, 1] or where the rows start with [0, 0, 1, 0, -1, 1] and the remaining terms are zeros.

Observation: the first 29 terms coincide with the first 29 terms of A161345 that are >= 21.

Apparently a(n)=A127329(n) for n>2. - R. J. Mathar, Sep 05 2023

Links

Table of n, a(n) for n=1..29.

Example

The symmetric representation of sigma(21) in the first quadrant looks like this:
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There are four parts (or polygons) and its second part is an octagon of width 1 and one of the vertices of the octagon is also the central vertex of the first valley of the largest Dyck path of the structure so 21 is in the sequence.

Crossrefs

Subsequence of A016945, A264102, A280107 and A364414.

Cf. A033676, A161345, A196020, A235791, A236104, A237270 (parts), A237271, A237591, A237593, A240062, A245092, A249351 (widths), A262626, A364639.

Sequence in context: A280107 A264102 A364414 * A352096 A103246 A206347

Adjacent sequences: A365078 A365079 A365080 * A365082 A365083 A365084

Keyword

nonn,more

Author

Omar E. Pol, Aug 20 2023

Status

approved