This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A269837 #19 Jul 10 2016 23:19:54
%S A269837 1,2,4,3,6,4,9,8,5,12,10,6,16,15,12,7,20,18,14,8,25,24,21,16,9,30,28,
%T A269837 24,18,10,36,35,32,27,20,11,42,40,36,30,22,12,49,48,45,40,33,24,13,56,
%U A269837 54,50,44,36,26,14,64,63,60,55,48,39,28,15
%N A269837 Irregular triangle read by rows: even terms of A094728(n+1) divided by 4.
%C A269837 See A264798 and A261046 for the Hydrogen atom and the Janet periodic table.
%C A269837 a(n) odd terms are again A264798.
%C A269837 Decomposition by multiplication i.e. a(n) = b(n)*c(n) by irregular triangle:
%C A269837 1, 1 1,
%C A269837 2, 1 2,
%C A269837 4, 3, 2, 1, 2, 3,
%C A269837 6, 4, = 2, 1, * 3, 4,
%C A269837 9, 8, 5, 3, 2, 1, 3, 4, 5,
%C A269837 12, 10, 6, 3, 2, 1, 4, 5, 6,
%C A269837 16, 15, 12, 7, 4, 3, 2, 1, 4, 5, 6, 7,
%C A269837 etc. etc. etc.
%C A269837 b(n) is duplicated A004736(n) or mirror of A122197(n+1). c(n) = A138099(n+1).
%C A269837 Decomposition by subtraction, a(n) = d(n) - e(n):
%C A269837 1, 1 0,
%C A269837 2, 2, 0,
%C A269837 4, 3, 4, 3, 0, 0,
%C A269837 6, 4, = 6, 5, - 0, 1,
%C A269837 9, 8, 5, 9, 8, 7, 0, 0, 2,
%C A269837 12, 10, 6, 12, 11, 10, 0, 1, 4,
%C A269837 16, 15, 12, 7, 16, 15, 14, 13, 0, 0, 2, 6,
%C A269837 20, 18, 14, 8, 20, 19, 18, 17, 0, 1, 4, 9,
%C A269837 etc. etc. etc.
%C A269837 d(n) is the natural numbers A000027 inverted by lines. e(n) will be studied (see A239873).
%C A269837 Sum of a(n) by diagonals: 1, 5, 13, 27, 48, ... . The third differences have the period 2: repeat 2, 1. See A002717.
%t A269837 Table[(n + 1)^2 - k^2, {n, 15}, {k, 0, n - 1}]/4 /. _Rational -> Nothing // Flatten (* _Michael De Vlieger_, Mar 07 2016 *)
%Y A269837 Cf. A000027, A000034, A002717, A004736, A094728, A122197, A138099, A167430, A239873, A261046, A264798.
%K A269837 nonn,tabf
%O A269837 0,2
%A A269837 _Paul Curtz_, Mar 06 2016