cp's OEIS Frontend

A194703 Triangle read by rows: T(k,m) = number of occurrences of k in the last section of the set of partitions of (3 + m).

%I A194703 #29 Sep 02 2023 20:32:56
%S A194703 3,2,1,0,1,2,1,0,1,1,0,1,0,1,1,0,0,1,0,1,1,3,2,1,0,1,2,1,0,1,1,0,1,0,
%T A194703 1,1,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0,
%U A194703 0,0,0,0,1,0,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0,0,0,0,0,0,0,1,0,1,1,0,0,0,0,0,0
%N A194703 Triangle read by rows: T(k,m) = number of occurrences of k in the last section of the set of partitions of (3 + m).
%C A194703 Sub-triangle of A182703 and also of A194812. Note that the sum of every row is also the number of partitions of 3. For further information see A182703 and A135010.
%F A194703 T(k,m) = A182703(3+m,k), with T(k,m) = 0 if k > 3+m.
%F A194703 T(k,m) = A194812(3+m,k).
%e A194703 Triangle begins:
%e A194703 3,
%e A194703 2, 1,
%e A194703 0, 1, 2,
%e A194703 1, 0, 1, 1,
%e A194703 0, 1, 0, 1, 1,
%e A194703 0, 0, 1, 0, 1, 1,
%e A194703 0, 0, 0, 1, 0, 1, 1,
%e A194703 0, 0, 0, 0, 1, 0, 1, 1,
%e A194703 0, 0, 0, 0, 0, 1, 0, 1, 1,
%e A194703 0, 0, 0, 0, 0, 0, 1, 0, 1, 1,
%e A194703 ...
%e A194703 For k = 1 and m = 1, T(1,1) = 3 because there are three parts of size 1 in the last section of the set of partitions of 4, since 3 + m = 4, so a(1) = 3.
%e A194703 For k = 2 and m = 1, T(2,1) = 2 because there are two parts of size 2 in the last section of the set of partitions of 4, since 3 + m = 4, so a(2) = 2.
%Y A194703 Always the sum of row k = p(3) = A000041(3) = 3.
%Y A194703 The first (0-10) members of this family of triangles are A023531, A129186, A194702, this sequence, A194704-A194710.
%Y A194703 Cf. A135010, A138121, A182712-A182714, A194812.
%K A194703 nonn,tabl
%O A194703 1,1
%A A194703 _Omar E. Pol_, Feb 05 2012