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a(n) is the number of ways n can be written as a sum of a practical number and two 11-gonal numbers.
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%I #11 Oct 10 2024 16:00:02

%S 1,2,2,2,1,2,1,2,1,1,0,2,3,2,1,2,2,3,2,3,1,1,2,3,1,2,1,3,2,4,3,5,2,3,

%T 2,3,2,3,2,3,2,6,4,2,1,2,3,3,3,3,2,2,2,4,2,2,2,3,4,5,5,5,2,4,4,6,4,3,

%U 1,4,5,4,4,2,3,4,4,6,3,3,3,3,3,4,3,4,3,4,6,7,4,4,1,4,4,6,6

%N a(n) is the number of ways n can be written as a sum of a practical number and two 11-gonal numbers.

%C Somu and Tran (2024) proved that a(n) > 0 for sufficiently large n.

%C Conjecture (checked up to 10^8): a(n) = 0 if and only if n = 11.

%H Duc Van Khanh Tran, <a href="/A375583/b375583.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. A005153, A051682.

%K nonn

%O 1,2

%A _Duc Van Khanh Tran_, Aug 19 2024