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Vorschau:
Calculating sequence element a(16) of OEIS A108235
Abstract The On-Line Encyclopedia of Integer Sequences (OEIS) lists under the identifier A108235 the following sequence: $a(n)=$ Number of partitions of $\{1,2,...,3n\}$ into $n$ triples $(X,Y,Z)$ each satisfying $X+Y=Z$. The following values can be found there (status on Apr 18 2020) \sourceon n a(n) 1 1 2 0 3 0 4 8 5 21 6 0 7 0 8 3040 9 20505 10 0 11 0 12 10567748 13 103372655 14 0 15 0 \sourceoff For example, $a(4)=8$, and there are the following eight partitions of set $\{1,2,...,12\}$. \sourceon No. 1 (1 5 6) (2 8 10) (3 9 12) (4 7 11) No. 2 (1 5 6) (2 9 11) (3 7 10) (4 8 12) No. 3 (1 6 7) (2 10 12) (3 8 11) (4 5 9) No. 4 (1 8 9) (2 10 12) (3 4 7) (5 6 11) No. 5 (1 9 10) (2 4 6) (3 8 11) (5 7 12) No. 6 (1 10 11) (2 5 7) (3 6 9) (4 8 12) No. 7 (1 11 12) (2 6 8) (3 7 10) (4 5 9) No. 8 (1 11 12) (2 7 9) (3 5 8) (4 6 10) \sourceoff Now we are happy to announce that we can add two more members to this sequence. The following holds. \[a(16)=142664107305\] \[a(17)=1836652173363\] Furthermore, we were able to calculate the member \(a'(43)\) for the related sequence A002849. \[a'(43)=16852166906\]
 
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