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%I #7 Jun 10 2026 23:43:20
%S 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,
%T 24,21,10,18,24,28,30,30,28,24,11,20,27,32,35,36,35,32,27,12,22,30,36,
%U 40,42,42,40,36,30,13,24,33,40,45,48,49,48,45,40,33
%N 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}.
%F T(p,q) = p*(q-2).
%e Rows begin:
%e p/q 3 4 5 6 7 8 9 10 ...
%e 3 3 6 9 12 15 18 21 24 ...
%e 4 4 8 12 16 20 24 28 32 ...
%e 5 5 10 15 20 25 30 35 40 ...
%e 6 6 12 18 24 30 36 42 48 ...
%e 7 7 14 21 28 35 42 49 56 ...
%e 8 8 16 24 32 40 48 56 64 ...
%e 9 9 18 27 36 45 54 63 72 ...
%e 10 10 20 30 40 50 60 70 80 ...
%e 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.
%K nonn,tabl,easy
%O 3,1
%A _John Mason_, Jun 05 2026