A396776 Square array read by upwards antidiagonals: T(p,q) is the number cells required to completely surround a single cell of the regular tiling with Schläfli symbol {p,q}.

3, 4, 6, 5, 8, 9, 6, 10, 12, 12, 7, 12, 15, 16, 15, 8, 14, 18, 20, 20, 18, 9, 16, 21, 24, 25, 24, 21, 10, 18, 24, 28, 30, 30, 28, 24, 11, 20, 27, 32, 35, 36, 35, 32, 27, 12, 22, 30, 36, 40, 42, 42, 40, 36, 30, 13, 24, 33, 40, 45, 48, 49, 48, 45, 40, 33

Offset

3,1

Links

Table of n, a(n) for n=3..68.

Formula

T(p,q) = p*(q-2).

Example

Rows begin:
p/q  3  4  5  6  7  8  9 10 ...
3    3  6  9 12 15 18 21 24 ...
4    4  8 12 16 20 24 28 32 ...
5    5 10 15 20 25 30 35 40 ...
6    6 12 18 24 30 36 42 48 ...
7    7 14 21 28 35 42 49 56 ...
8    8 16 24 32 40 48 56 64 ...
9    9 18 27 36 45 54 63 72 ...
10  10 20 30 40 50 60 70 80 ...
For example, a single square on the Euclidean plane, {4,4}, requires 8 cells to completely surround it. On the {4,5} hyperbolic plane, 12 cells are required.

Crossrefs

Sequence in context: A372784 A016655 A057757 * A379348 A336717 A332361

Adjacent sequences: A396770 A396771 A396772 * A396777 A396778 A396780

Keyword

nonn,tabl,easy

Author

John Mason, Jun 05 2026

Status

approved