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A098489 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.

%I A098489 #15 Sep 19 2019 07:57:40
%S A098489 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 A098489 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 A098489 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 A098489 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 A098489 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 A098489 Triangle begins:
%e A098489   {1}
%e A098489   {0,0}
%e A098489   {0,1}
%e A098489   {0,0,1}
%e A098489   {0,1,1}
%e A098489   {0,1,2}
%e A098489   {0,2,3,0}
%e A098489   ...
%e A098489 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 A098489 Differs from A098490 in rows with triangular index. Cf. A098493.
%Y A098489 Row sums are in A098491.
%K A098489 nonn,tabf
%O A098489 0,14
%A A098489 _Ralf Stephan_, Sep 12 2004