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%I #49 Jun 29 2023 09:51:39
%S 1,1,1,1,1,1,1,1,1,1,3,4,9,14,19,16,9,4,1,1,1,1,1,3,7,21,72,269,994,
%T 3615
%N Irregular triangle: T(n,k) gives the number of k-polysticks on edges of the n-cube up to isometries of the n-cube, with 0 <= k <= A001787(n).
%H Code Golf Stack Exchange, <a href="https://codegolf.stackexchange.com/q/201054/53884">Counting polyominoes on (hyper-)cubes</a>
%H Peter Kagey, <a href="/A333333/a333333.pdf">Examples of T(3,3) through T(3,8)</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hypercube">Hypercube</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Polystick">Polystick</a>
%F T(n,k) = T(n-1,k) for k < n.
%F T(n,0) = T(n,1) = T(n,2) = T(n,A001787(n)-1) = T(n,A001787(n)) = 1.
%F A222192(n) = Sum_{k=0..n*2^(n-1)} T(n,k) - Sum_{k=0..(n-1)*2^(n-2)} T(n-1,k) for n >= 2. - _Peter Kagey_, Jun 19 2023
%e Table begins:
%e n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 ...
%e ---+---------------------------------------------------
%e 1| 1, 1;
%e 2| 1, 1, 1, 1, 1;
%e 3| 1, 1, 1, 3, 4, 9, 14, 19, 16, 9, 4, 1, 1;
%e 4| 1, 1, 1, 3, 7, 21, 72, 269, 994, 3615, ...
%Y Cf. A001787, A222192.
%K nonn,more,tabf
%O 1,11
%A _Peter Kagey_, Mar 15 2020
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