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%I #6 Jan 27 2022 21:00:53
%S 1,1,2,2,4,7,2,6,9,11,2,6,11,14,18
%N Triangle read by rows: T(n,k) is the maximum number that can be reached following the rules of the stepping stone puzzle of A337663 restricted to the n X k grid, allowing any number of initial 1's, 1 <= k <= n.
%C The possible numbers of initial 1's required to reach T(n,k) are not always consecutive. For n = 5 and k = 2, 2 or 4 initial 1's are required to reach T(5,2) = 6.
%e Triangle begins:
%e n\k| 1 2 3 4 5
%e ---+--------------
%e 1 | 1
%e 2 | 1 2
%e 3 | 2 4 7
%e 4 | 2 6 9 11
%e 5 | 2 6 11 14 18
%e For n = k = 4, T(4,4) = 11 can be reached by starting with 2, 3, 4, or 5 1's:
%e 9 1 10 . 1 11 1 9 1 11 1 8 1 11 1 6
%e 6 2 7 . 7 . 2 6 9 . . 7 8 . 1 4
%e . 3 1 . 5 1 3 . 6 2 1 5 5 2 1 1
%e 11 8 4 5 10 4 8 . 3 1 4 10 10 3 7 9
%Y Cf. A337663, A350765.
%K nonn,tabl,more
%O 1,3
%A _Pontus von Brömssen_, Jan 14 2022
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