A124171 Sequence obtained by reading the triangles shown below by rows.

1, 1, 2, 3, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 1, 2, 3

Offset: 1

Author

Colm Mulcahy, Dec 05 2006

Keywords

• nonn
• tabf
• easy

Comments

It appears that this is also a triangle read by rows in which row n lists the first A000217(n) positive integers, n >= 1 (see example, second part). - Omar E. Pol, May 29 2012

Examples

			1
1
2 3
1
2 3
4 5 6
1
2 3
4 5 6
7 8 9 10
1
2 3
4 5 6
7 8 9 10
11 12 13 14 15
From _Omar E. Pol_, May 29 2012: (Start)
Written as an irregular triangle the sequence begins:
1;
1, 2, 3;
1, 2, 3, 4, 5, 6;
1, 2, 3, 4, 5, 6, 7, 8, 9, 10;
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15;
Row n has length A000217(n). (End)
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

See A115215 for another version.

Programs

Maple

A000217 := proc(n) n*(n+1)/2 ; end : for t from 1 to 10 do for i from 1 to A000217(t) do printf("%d, ",i) ; od ; od ; # R. J. Mathar, May 18 2007

Mathematica

Table[Range[(t(t+1))/2],{t,10}]//Flatten (* Harvey P. Dale, Aug 06 2025 *)

Python

from math import comb
from sympy import integer_nthroot
def A124171(n): return n-comb((m:=integer_nthroot(6*n,3)[0])+(n>comb(m+2,3))+1,3) # Chai Wah Wu, Nov 10 2024

Extensions

More terms from R. J. Mathar, May 18 2007