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Triangle read by rows: T(n,k) = number of parts in the k-th region of n.
16

%I #16 Mar 30 2012 17:34:05

%S 1,1,2,1,2,3,1,2,3,1,5,1,2,3,1,5,1,7,1,2,3,1,5,1,7,1,2,1,11,1,2,3,1,5,

%T 1,7,1,2,1,11,1,2,1,15,1,2,3,1,5,1,7,1,2,1,11,1,2,1,15,1,2,1,4,1,1,22,

%U 1,2,3,1,5,1,7,1,2,1,11,1,2,1,15

%N Triangle read by rows: T(n,k) = number of parts in the k-th region of n.

%e Triangle begins:

%e 1;

%e 1,2;

%e 1,2,3;

%e 1,2,3,1,5;

%e 1,2,3,1,5,1,7;

%e 1,2,3,1,5,1,7,1,2,1,11;

%e 1,2,3,1,5,1,7,1,2,1,11,1,2,1,15;

%e 1,2,3,1,5,1,7,1,2,1,11,1,2,1,15,1,2,1,4,1,1,22;

%e ...

%e Row n has length A000041(n). Row sums give A006128, n >= 1. Right border gives A000041, n >= 1. Records in every row give A000041, n >= 1. Rows converge to A194446.

%Y Cf. A000041, A006128, A135010, A138121, A186114, A186412, A193870, A194437, A194438, A194439, A194446, A194447.

%K nonn,tabf

%O 1,3

%A _Omar E. Pol_, Nov 27 2011