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A233292 Triangle read by rows: T(n,k) is the number of partitions of n into at most four parts in which no part exceeds k, 0 <= k <= n.

%I A233292 #21 Feb 24 2022 08:45:48
%S A233292 1,0,1,0,1,2,0,1,2,3,0,1,3,4,5,0,0,2,4,5,6,0,0,2,5,7,8,9,0,0,1,4,7,9,
%T A233292 10,11,0,0,1,4,8,11,13,14,15,0,0,0,3,7,11,14,16,17,18,0,0,0,2,7,12,16,
%U A233292 19,21,22,23,0,0,0,1,5,11,16,20,23,25,26,27,0,0,0,1,5,11,18,23,27,30,32,33,34
%N A233292 Triangle read by rows: T(n,k) is the number of partitions of n into at most four parts in which no part exceeds k, 0 <= k <= n.
%C A233292 Transpose of table A219237.
%F A233292 T(n,k) = Sum_{j=0..k} A232539(n,j).
%e A233292 Triangle T(n,k) begins:
%e A233292 1;
%e A233292 0, 1;
%e A233292 0, 1, 2;
%e A233292 0, 1, 2, 3;
%e A233292 0, 1, 3, 4, 5;
%e A233292 0, 0, 2, 4, 5,  6;
%e A233292 0, 0, 2, 5, 7,  8,  9;
%e A233292 0, 0, 1, 4, 7,  9, 10, 11;
%e A233292 0, 0, 1, 4, 8, 11, 13, 14, 15; ...
%Y A233292 Cf. A001400 (main diagonal), A219237, A232539.
%K A233292 nonn,tabl
%O A233292 0,6
%A A233292 _L. Edson Jeffery_, Jan 02 2014