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 A337787 #18 Sep 22 2020 03:54:21
%S A337787 1,1,1,2,1,2,1,3,1,3,2,4,1,5,1,6,3,5,2,8,2,8,4,8,3,12,3,11,6,11,5,15,
%T A337787 4,16,9,14,7,20,8,18,11,20,12,25,8,25,18,24,12,31,16,32,19,29,21,39,
%U A337787 19,36,28,38,25,47,25,46,33,46,34,55,31,56,44,55,39,67,42,66,52,66,53,76,50,81,65,77,57
%N A337787 Number of addition triangles whose sum is n (version 2).
%C A337787 An addition triangle has any set of positive numbers as base; other rows are formed by adding pairs of adjacent numbers.
%C A337787 Reversing the base does not count as a different triangle.
%H A337787 Seiichi Manyama, <a href="/A337787/b337787.txt">Table of n, a(n) for n = 1..500</a>
%e A337787 n |
%e A337787 -----+-------------------------------
%e A337787 1 | 1
%e A337787 -----+-------------------------------
%e A337787 2 | 2
%e A337787 -----+-------------------------------
%e A337787 3 | 3
%e A337787 -----+-------------------------------
%e A337787 4 | 2
%e A337787 | 4 1,1
%e A337787 -----+-------------------------------
%e A337787 5 | 5
%e A337787 -----+-------------------------------
%e A337787 6 | 3
%e A337787 | 6 1,2
%e A337787 -----+-------------------------------
%e A337787 7 | 7
%e A337787 -----+-------------------------------
%e A337787 8 | 4 4
%e A337787 | 8 1,3 2,2
%e A337787 -----+-------------------------------
%e A337787 9 | 9
%e A337787 -----+-------------------------------
%e A337787 10 | 5 5
%e A337787 | 10 1,4 2,3
%e A337787 -----+-------------------------------
%e A337787 11 | 4
%e A337787 | 2,2
%e A337787 | 11 1,1,1
%e A337787 -----+-------------------------------
%e A337787 12 | 6 6 6
%e A337787 | 12 1,5 2,4 3,3
%e A337787 -----+-------------------------------
%e A337787 13 | 13
%e A337787 -----+-------------------------------
%e A337787 14 | 5
%e A337787 | 7 7 7 2,3
%e A337787 | 14 1,6 2,5 3,4 1,1,2
%e A337787 -----+-------------------------------
%e A337787 15 | 15
%e A337787 -----+-------------------------------
%e A337787 16 | 6
%e A337787 | 8 8 8 8 3,3
%e A337787 | 16 1,7 2,6 3,5 4,4 1,2,1
%e A337787 -----+-------------------------------
%e A337787 17 | 6 6
%e A337787 | 2,4 3,3
%e A337787 | 17 1,1,3 2,1,2
%e A337787 -----+-------------------------------
%e A337787 18 | 9 9 9 9
%e A337787 | 18 1,8 2,7 3,6 4,5
%e A337787 -----+-------------------------------
%e A337787 19 | 7
%e A337787 | 3,4
%e A337787 | 19 1,2,2
%o A337787 (Ruby)
%o A337787 def f(n)
%o A337787 ary = [1]
%o A337787 (n - 1).times{|i|
%o A337787 ary = [0] + ary + [0]
%o A337787 ary = (0..i + 1).map{|j| ary[j] + ary[j + 1] + 1}
%o A337787 }
%o A337787 ary
%o A337787 end
%o A337787 def A(n)
%o A337787 f_ary = (1..n / 2).map{|i| [i]}
%o A337787 cnt = 2
%o A337787 s = 1
%o A337787 while f_ary.size > 0
%o A337787 s_ary = f(s + 1)
%o A337787 b_ary = []
%o A337787 f_ary.each{|i|
%o A337787 (1..i[0] - 1).each{|j|
%o A337787 a = [j]
%o A337787 (0..s - 1).each{|k|
%o A337787 num = i[k] - a[k]
%o A337787 if num > 0
%o A337787 a << num
%o A337787 else
%o A337787 break
%o A337787 end
%o A337787 }
%o A337787 if a.size == s + 1
%o A337787 sum = (0..s).inject(0){|t, m| t + s_ary[m] * a[m]}
%o A337787 if sum < n
%o A337787 b_ary << a
%o A337787 elsif sum == n
%o A337787 cnt += 1
%o A337787 cnt += 1 if a == a.reverse
%o A337787 end
%o A337787 end
%o A337787 }
%o A337787 }
%o A337787 f_ary = b_ary
%o A337787 s += 1
%o A337787 end
%o A337787 cnt / 2
%o A337787 end
%o A337787 def A337787(n)
%o A337787 (1..n).map{|i| A(i)}
%o A337787 end
%o A337787 p A337787(50)
%Y A337787 Cf. A014430, A062684, A062896, see A337785 for version 1.
%K A337787 nonn,look
%O A337787 1,4
%A A337787 _Seiichi Manyama_, Sep 21 2020