A271439 If n is a triangular number, a(n) = 0, otherwise a(n) = n - A002024(n) + 1.

0, 0, 1, 0, 2, 3, 0, 4, 5, 6, 0, 7, 8, 9, 10, 0, 11, 12, 13, 14, 15, 0, 16, 17, 18, 19, 20, 21, 0, 22, 23, 24, 25, 26, 27, 28, 0, 29, 30, 31, 32, 33, 34, 35, 36, 0, 37, 38, 39, 40, 41, 42, 43, 44, 45, 0, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 0, 56, 57, 58

Offset: 0

Author

Peter Kagey, Apr 07 2016

Keywords

• nonn
• tabl

Comments

a(n) gives the number above n when the natural numbers are represented as a square array, or 0 if n is in the top row.

1 3 6 10

2 5 9

4 8

7

Examples

			As a regular triangle, sequence begins:
  0;
  0, 1;
  0, 2, 3;
  0, 4, 5, 6;
  0, 7, 8, 9, 10;
  ...
		

Links

• Peter Kagey, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000217 (right diagonal), A006003 (row sums).

Programs

Mathematica

Riffle[#, 0] &@ Map[# (# - 1)/2 + Range@ # &, Range[0, 11]] /. {} -> {0} // Flatten (* Michael De Vlieger, Apr 07 2016 *)

Python

from math import isqrt
def A271439(n): return n-m+(kChai Wah Wu, Nov 07 2024