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a(n) is the smallest number which can be represented as the sum of n distinct nonzero triangular numbers in exactly n ways, or 0 if no such number exists.
3

%I #9 Dec 27 2021 02:44:16

%S 1,16,37,64,83,128,177,204,270,352,430,533,632,764,893,1102,1256,1443,

%T 1630,1855,2141,2384,2699,3053,3378,3753,4176,4620,5068,5570,6107,

%U 6654,7253,7904,8526,9241,9975,10699,11533,12401,13301,14189,15179,16233,17286,18412

%N a(n) is the smallest number which can be represented as the sum of n distinct nonzero triangular numbers in exactly n ways, or 0 if no such number exists.

%e For n = 2: 16 = 1 + 15 = 6 + 10.

%e For n = 3: 37 = 1 + 15 + 21 = 3 + 6 + 28 = 6 + 10 + 21.

%Y Cf. A000217, A265134, A307597, A307598, A341021-A341027, A342326, A350241.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Dec 23 2021

%E More terms from _Jinyuan Wang_, Dec 26 2021