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Triangle read by rows: T(1,1)=1, T(n,k) = T(n,k+1)+T(n-k,max(2*floor(k/2)-1,1)) and T(n,k) = 0 if k > A316355(n).
4

%I #26 Jun 30 2018 09:45:09

%S 1,1,2,1,4,2,1,7,3,1,13,6,2,24,11,4,45,21,8,1,84,39,15,2,1,156,72,27,

%T 3,1,291,135,51,6,2,543,252,96,12,4,1013,470,179,23,8,1889,876,333,42,

%U 15,3524,1635,622,79,28,1,6575,3051,1162,149,53,2,1,12266,5691

%N Triangle read by rows: T(1,1)=1, T(n,k) = T(n,k+1)+T(n-k,max(2*floor(k/2)-1,1)) and T(n,k) = 0 if k > A316355(n).

%H Seiichi Manyama, <a href="/A316354/b316354.txt">Rows n = 1..402, flattened</a>

%e n\k | 1 2 3 4 5

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

%e 1 | 1;

%e 2 | 1;

%e 3 | 2, 1;

%e 4 | 4, 2, 1;

%e 5 | 7, 3, 1;

%e 6 | 13, 6, 2;

%e 7 | 24, 11, 4;

%e 8 | 45, 21, 8, 1;

%e 9 | 84, 39, 15, 2, 1;

%e 10 | 156, 72, 27, 3, 1;

%Y Columns 1,2 give A224704, A316356 (for n>0).

%Y Cf. A052928, A288267, A316355.

%K nonn,tabf

%O 1,3

%A _Seiichi Manyama_, Jun 30 2018