A131507 2n+1 appears n+1 times.

1, 3, 3, 5, 5, 5, 7, 7, 7, 7, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 15, 15, 15, 17, 17, 17, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23

Offset: 0

Author

Paul Curtz, Aug 13 2007

Keywords

• nonn
• tabl

Comments

Sum of terms of row n is (n+1)*(2n+1) = A000384(n+1). - Michel Marcus, Feb 02 2014

Where records occur give A000217. - Omar E. Pol, Nov 05 2015

Examples

			As a triangle, the sequence starts:
1;
3, 3;
5, 5, 5;
7, 7, 7, 7;
9, 9, 9, 9, 9;
...
		

Links

• Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened

Crossrefs

Cf. A000217, A002024, A003056, A005408.

Cf. A001650.

Programs

Haskell

a131507 n k = a131507_tabl !! n !! k
a131507_row n = a131507_tabl !! n
a131507_tabl = zipWith ($) (map replicate [1..]) [1, 3 ..]
a131507_list = concat a131507_tabl
-- Reinhard Zumkeller, Jul 12 2014, Mar 18 2011
(Chipmunk BASIC v3.6.4(b8)) # http://www.nicholson.com/rhn/basic/
for n=1 to 23 step 2
for j=1 to n  step 2
print str$(n)+", ";
next j : next n : print
end
# Jeremy Gardiner, Feb 02 2014

Maple

seq(2*floor(sqrt(2*n+1)+1/2)-1, n=0..70); # Ridouane Oudra, Oct 20 2019

Mathematica

Table[2 n + 1, {n, 0, 11}, {n + 1}] // Flatten (* Michael De Vlieger, Nov 05 2015 *)

Python

from math import isqrt
def A131507(n): return (k:=isqrt(m:=n+1<<1))+(m>k*(k+1))-1<<1|1 # Chai Wah Wu, Nov 04 2024

Formula

a(n) = 2*floor(sqrt(2n+1)+1/2) - 1. - Ridouane Oudra, Oct 20 2019