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%I #15 Sep 19 2019 07:57:40
%S 1,0,0,0,1,0,0,1,0,1,1,0,1,2,0,2,3,0,0,2,3,1,0,2,4,2,1,2,4,4,0,4,7,3,
%T 1,0,3,8,7,1,1,3,9,10,2,0,4,12,12,4,0,5,14,15,7,2,5,13,21,11,0,0,6,19,
%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
%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 even 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 begins:
%e {1}
%e {0,0}
%e {0,1}
%e {0,0,1}
%e {0,1,1}
%e {0,1,2}
%e {0,2,3,0}
%e ...
%e 6 is 1+1+1+3, 1+1+2+2, 1+5, 2+4, 3+3 with even number of parts and no part more than thrice. Two of these partitions have one part occurring once or twice and (the middle) three have two such parts. The 6th row is therefore 0,2,3,0.
%Y Differs from A098490 in rows with triangular index. Cf. A098493.
%Y Row sums are in A098491.
%K nonn,tabf
%O 0,14
%A _Ralf Stephan_, Sep 12 2004