A334007 a(n) is the least integer that can be expressed as the sum of one or more consecutive nonzero triangular numbers in exactly n ways.

1, 10, 2180, 10053736, 13291443468940

Offset: 1

Author

Ilya Gutkovskiy, Apr 12 2020

Keywords

• nonn
• hard
• more

Examples

			Let S(k, m) denote the sum of m triangular numbers starting from k(k+1)/2. We have
a(1) = S(1, 1);
a(2) = S(4, 1) = S(1, 3);
a(3) = S(31, 4) = S(27, 5) = S(9, 15);
a(4) = S(945, 22) = S(571, 56) = S(968, 21) = S(131, 266);
a(5) = S(4109, 38947) = S(25213, 20540) = S(10296, 32943) = S(32801, 15834) = S(31654, 16472).
		

Links

• Eric Weisstein's World of Mathematics, Triangular Number
• Index to sequences related to polygonal numbers

Crossrefs

Cf. A000217, A054859, A068314, A034706, A050943, A186337, A298467, A307666, A309783, A334008, A334010, A334011, A334012.

Extensions

a(5) from Giovanni Resta, Apr 13 2020