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

1,3

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

Links

Table of n, a(n) for n=1..87.

Example

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)

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

Prog

(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

Crossrefs

See A115215 for another version.

Sequence in context: A071797 A338027 A025481 * A276146 A210530 A076645

Adjacent sequences: A124168 A124169 A124170 * A124172 A124173 A124174

Keyword

nonn,tabf,easy

Author

Colm Mulcahy, Dec 05 2006

Extensions

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

Status

approved