A370615 a(0) = 0. For n >= 1, a(n) = 1 + (sum of the next consecutive a(n-1) positive integers).

0, 1, 2, 6, 40, 1181, 755841, 286577870992, 41063655031092356251961, 843111882268046256673070172994877712169680285, 355418823010783945962646271385485944012152783545060852031848083841154141557381002556807596

Offset: 0

Author

Paolo Xausa, Apr 30 2024

Keywords

• nonn

Examples

			0, 0+1 = 1, 1+1 = 2, 2+3+1 = 6, 4+5+...+9+1 = 40, 10+11+...+49+1 = 1181, ...
   |        |        \_/        \_______/         \__________/
0 terms  1 term    2 terms       6 terms            40 terms
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..13

Crossrefs

Partial sums give A372421.

Programs

Mathematica

Block[{k = 0}, Differences[NestList[PolygonalNumber[#] + k++ &, 0, 12]]]

Formula

a(0) = 0. For n >= 1, a(n) = A372421(n) - A372421(n-1).