A370615 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

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

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

CROSSREFS

Partial sums give A372421.

Sequence in context: A320489 A135755 A337699 * A051185 A118623 A000612

Adjacent sequences: A370612 A370613 A370614 * A370616 A370617 A370618

KEYWORD

nonn

AUTHOR

Paolo Xausa, Apr 30 2024

STATUS

approved