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

%I #18 Jan 17 2016 20:58:34

%S 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,

%T 99,91,75,51,19,121,117,105,85,57,21,143,135,119,95,63,23,169,165,153,

%U 133,105,69,25,195,187,171,147,115,75,27,225,221,209,189,161,125,81,29,255,247

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

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

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

%C First column: A085046(n+1).

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

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

%e Irregular triangle begins:

%e 1,

%e 3,

%e 9, 5,

%e 15, 7,

%e 25, 21, 9,

%e 35, 27, 11,

%e 49, 45, 33, 13,

%e 63, 55, 39, 15,

%e ...

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

%o (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

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

%K nonn,easy,tabf

%O 0,2

%A _Paul Curtz_, Nov 25 2015