A391817 Number of topological sequences of three dimensional lattice points with index n and depth n - 2.

1, 9, 25, 61, 125, 252, 472, 872, 1548

Offset

5,2

Comments

See A387672 for the definition of a topological sequence.

Links

Table of n, a(n) for n=5..13.

Example

a(5) = 1: {(0, 0, 0), (1, 0, 0), (0, 1, 0)}.
a(6) = 9:
 {(0, 0, 0), (0, 1, 0), (0, 0, 1), (0, 1, 1)},
 {(0, 0, 0), (0, 1, 0), (0, 0, 1), (0, 2, 0)},
 {(0, 0, 0), (0, 1, 0), (0, 0, 1), (1, 0, 0)},
 {(0, 0, 0), (1, 0, 0), (0, 0, 1), (0, 1, 0)},
 {(0, 0, 0), (1, 0, 0), (0, 0, 1), (1, 0, 1)},
 {(0, 0, 0), (1, 0, 0), (0, 0, 1), (2, 0, 0)},
 {(0, 0, 0), (1, 0, 0), (0, 1, 0), (0, 2, 0)},
 {(0, 0, 0), (1, 0, 0), (0, 1, 0), (1, 1, 0)},
 {(0, 0, 0), (1, 0, 0), (0, 1, 0), (2, 0, 0)}.

Crossrefs

Third diagonal of A387672.

Cf. A000219, A000293, A002836, A207542.

Sequence in context: A147497 A147353 A049740 * A147405 A111440 A077118

Adjacent sequences: A391814 A391815 A391816 * A391818 A391819 A391820

Keyword

nonn,more

Author

John Tyler Rascoe, Dec 20 2025

Status

approved