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a(n) = A184218(n)/A130703(n) unless A130703(n) = 0 in which case a(n) = 0.
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%I #7 Mar 30 2012 17:25:56

%S 0,0,0,0,1,1,2,1,1,2,3,1,1,5,4,1,5,4,5,7,1,5,9,5,1,9,10,1,9,7,8,11,1,

%T 14,11,1,7,13,10,1,13,10,11,15,1,11,20,7,5,18,14,5,17,22,14,19,11,14,

%U 19,1,1,27,16,13,27,16,26,23

%N a(n) = A184218(n)/A130703(n) unless A130703(n) = 0 in which case a(n) = 0.

%C a(n) is the "level" of triangular numbers.

%C The decomposition of triangular numbers into weight * level + gap is A000217(n) = A130703(n) * a(n) + (n + 1) if a(n) > 0.

%C A184218(n) = A000217(n) - (n + 1) if A000217(n) - (n + 1) > (n + 1), 0 otherwise.

%H Rémi Eismann, <a href="/A184219/b184219.txt">Table of n, a(n) for n = 1..10000</a>

%e For n = 3 we have A130703(3) = 0, hence a(3) = 0.

%e For n = 5 we have A184218(5)/A130703(5) = 9 / 9 = 1, hence a(5) = 1.

%e For n = 24 we have A184218(24)/A130703(24) = 275 / 55 = 5, hence a(24) = 5.

%Y Cf. A000217, A000027, A130703, A184218, A118534, A117078, A117563, A001223.

%K nonn

%O 1,7

%A _Rémi Eismann_, Jan 10 2011