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%I #6 Jul 05 2024 17:09:16
%S 1,2,2,2,1,2,2,4,2,2,1,2,3,3,1,3,3,5,3,4,2,4,3,4,3,2,3,3,3,6,5,6,4,5,
%T 4,7,4,4,3,5,3,6,3,5,4,6,6,7,6,4,4,6,4,6,5,4,7,7,3,6,7,7,6,7,3,8,5,7,
%U 6,7,6,8,6,7,7,8,4,8,7,6
%N a(n) is the number of ways n can be written as a sum of a practical number and two hexagonal numbers.
%C Somu and Tran (2024) proved that a(n) > 0 for sufficiently large n and conjectured that a(n) > 0 for all n > 0. The conjecture was checked up to 10^8.
%H Duc Van Khanh Tran, <a href="/A373688/b373688.txt">Table of n, a(n) for n = 1..10000</a>
%H Sai Teja Somu and Duc Van Khanh Tran, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL27/Somu/somu5.html">On sums of practical numbers and polygonal numbers</a>, Journal of Integer Sequences, 27(5), 2024.
%Y Cf. A000384, A005153.
%K nonn
%O 1,2
%A _Duc Van Khanh Tran_, Jun 13 2024