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

%I A264798 #18 Jan 17 2016 20:58:34
%S A264798 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 A264798 99,91,75,51,19,121,117,105,85,57,21,143,135,119,95,63,23,169,165,153,
%U A264798 133,105,69,25,195,187,171,147,115,75,27,225,221,209,189,161,125,81,29,255,247
%N A264798 Irregular triangle read by rows: odd-valued terms of A094728(n+1).
%C A264798 A094728(n+1) comes from A120070(n+2). a(n) approximates frequencies of the spectral lines of the hydrogen atom.
%C A264798 Row sums: 1, 3, 14, 22, ... = A024598(n+1).
%C A264798 First column: A085046(n+1).
%C A264798 Row sums of A261046(n) = 1, 3, 8, 12, ... = A014255(n). See the formula.
%F A264798 a(n) = A261046(n)*A167268(n+1)/2, where A167268 is Janet's sequence.
%e A264798 Irregular triangle begins:
%e A264798 1,
%e A264798 3,
%e A264798 9,  5,
%e A264798 15, 7,
%e A264798 25, 21,  9,
%e A264798 35, 27, 11,
%e A264798 49, 45, 33, 13,
%e A264798 63, 55, 39, 15,
%e A264798 ...
%t A264798 Table[n^2 - k^2, {n, 14}, {k, 0, n - 1}] /. n_ /; EvenQ@ n -> Nothing // Flatten (* _Michael De Vlieger_, Nov 25 2015 *)
%o A264798 (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 A264798 Cf. A014255, A024598, A085046, A094728, A120070, A167268, A249947, A261046.
%K A264798 nonn,easy,tabf
%O A264798 0,2
%A A264798 _Paul Curtz_, Nov 25 2015