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%I #14 Sep 19 2019 07:57:47
%S 0,0,1,0,1,1,1,0,0,1,1,0,1,2,1,1,1,1,0,2,3,1,0,2,4,2,1,2,4,4,0,1,7,6,
%T 0,0,3,8,7,1,1,3,9,10,2,0,4,12,12,4,0,5,14,15,7,1,3,18,23,7,1,0,6,19,
%U 26,14,1,0,7,22,32,20,2,2,6,24,42,26,4,0,8,30,49,35,7,0,8,36,60,44
%N Triangle T(n,k) read by rows: partitions of n with parts occurring at most thrice, k parts occurring once or twice and an odd number of parts.
%H Alex Fink, Richard K. Guy, and Mark Krusemeyer, <a href="https://doi.org/10.11575/cdm.v3i2.61940">Partitions with parts occurring at most thrice</a>, Contributions to Discrete Mathematics, Vol 3, No 2 (2008), pp. 76-114.
%e Triangle starts:
%e {1}
%e {0,1}
%e {0,1}
%e {1,1,0}
%e {0,1,1}
%e {0,1,2}
%e {1,1,1,1}
%e ...
%e 6 is 2+2+2, 6, 1+1+4, 1+2+3, with odd number of parts and no part more than thrice. The number of parts occurring once or twice in these partitions is 0,1,2,3, respectively. The 6th row is therefore 1,1,1,1.
%Y Differs from A098489 in rows with triangular index. Cf. A094893.
%Y Row sums are in A098492.
%K nonn,tabf
%O 0,14
%A _Ralf Stephan_, Sep 12 2004
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