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A374274 a(n) is the smallest number which can be represented as the sum of four distinct nonzero n-gonal numbers in exactly n ways, or -1 if no such number exists.

%I A374274 #14 Feb 16 2025 08:34:07
%S A374274 47,142,344,652,834,1542,2263,3090,4792,4570,5844,8480,9571,10542,
%T A374274 15892,18202,19587,23166,26732,32040,36371,39730,44709,52940,55141,
%U A374274 60362,67705,79624,86906,89266,103591,116246,126610,131462,135324,148190,158152,162422,186126,200254
%N A374274 a(n) is the smallest number which can be represented as the sum of four distinct nonzero n-gonal numbers in exactly n ways, or -1 if no such number exists.
%H A374274 Michael S. Branicky, <a href="/A374274/b374274.txt">Table of n, a(n) for n = 3..204</a>
%H A374274 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolygonalNumber.html">Polygonal Number</a>
%e A374274 a(3) = 47 = 1 + 3 + 15 + 28 = 1 + 10 + 15 + 21 = 3 + 6 + 10 + 28.
%e A374274 a(4) = 142 = 1^2 + 2^2 + 4^2 + 11^2 = 1^2 + 4^2 + 5^2 + 10^2 = 2^2 + 5^2 + 7^2 + 8^2 = 3^2 + 4^2 + 6^2 + 9^2.
%Y A374274 Cf. A025417, A057145, A350405, A374144, A374273.
%K A374274 nonn
%O A374274 3,1
%A A374274 _Ilya Gutkovskiy_, Jul 02 2024
%E A374274 a(36) and beyond from _Michael S. Branicky_, Jul 08 2024