A264798 Irregular triangle read by rows: odd-valued terms of A094728(n+1).

1, 3, 9, 5, 15, 7, 25, 21, 9, 35, 27, 11, 49, 45, 33, 13, 63, 55, 39, 15, 81, 77, 65, 45, 17, 99, 91, 75, 51, 19, 121, 117, 105, 85, 57, 21, 143, 135, 119, 95, 63, 23, 169, 165, 153, 133, 105, 69, 25, 195, 187, 171, 147, 115, 75, 27, 225, 221, 209, 189, 161, 125, 81, 29, 255, 247

Offset: 0

Author

Paul Curtz, Nov 25 2015

Keywords

• nonn
• easy
• tabf

Comments

A094728(n+1) comes from A120070(n+2). a(n) approximates frequencies of the spectral lines of the hydrogen atom.

Row sums: 1, 3, 14, 22, ... = A024598(n+1).

First column: A085046(n+1).

Row sums of A261046(n) = 1, 3, 8, 12, ... = A014255(n). See the formula.

Examples

			Irregular triangle begins:
1,
3,
9,  5,
15, 7,
25, 21,  9,
35, 27, 11,
49, 45, 33, 13,
63, 55, 39, 15,
...
		

Crossrefs

Cf. A014255, A024598, A085046, A094728, A120070, A167268, A249947, A261046.

Programs

Mathematica

Table[n^2 - k^2, {n, 14}, {k, 0, n - 1}] /. n_ /; EvenQ@ n -> Nothing // Flatten (* Michael De Vlieger, Nov 25 2015 *)

PARI

for(n=1,20,for(k=0,n-1,s=n^2-k^2;if(s%2,print1(s,", ")))) \\ Derek Orr, Dec 24 2015

Formula

a(n) = A261046(n)*A167268(n+1)/2, where A167268 is Janet's sequence.