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Triangle read by rows: T(n,k) is the length of the longest induced path in the n-dimensional hypercube, such that the end points of the path are at Hamming distance k, 0 <= k <= n.
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%I #7 Oct 02 2022 08:34:07

%S 0,0,1,0,1,2,0,1,4,3,0,1,6,7,4,0,1,12,13,12,11,0,1,26,25,24,25,24

%N Triangle read by rows: T(n,k) is the length of the longest induced path in the n-dimensional hypercube, such that the end points of the path are at Hamming distance k, 0 <= k <= n.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Snake-in-the-box">Snake-in-the-box</a>.

%e Triangle begins:

%e n\k| 0 1 2 3 4 5 6

%e ---+--------------------

%e 0 | 0

%e 1 | 0 1

%e 2 | 0 1 2

%e 3 | 0 1 4 3

%e 4 | 0 1 6 7 4

%e 5 | 0 1 12 13 12 11

%e 6 | 0 1 26 25 24 25 24

%Y Cf. A099155 (row maxima), A357360 (main diagonal).

%K nonn,tabl,more,hard

%O 0,6

%A _Pontus von Brömssen_, Oct 01 2022