A337766 Number of addition triangles with apex n where all rows are strongly increasing.
1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 8, 9, 10, 11, 13, 14, 16, 17, 19, 22, 24, 25, 28, 31, 33, 35, 39, 43, 46, 48, 52, 57, 60, 63, 69, 75, 78, 82, 88, 94, 99, 104, 111, 119, 124, 129, 137, 147, 153, 160, 169, 179, 187, 194, 204, 216, 224, 233, 246, 259, 267, 277, 292, 308, 318, 329, 343, 361
Offset: 1
Keywords
Examples
For n = 5: 5 5 1,4 2,3 5 For n = 6: 6 6 1,5 2,4 6 For n = 7: 7 7 7 1,6 2,5 3,4 7 For n = 8: 8 3,5 8 8 8 1,2,3 1,7 2,6 3,5 8 For n = 9: 9 3,6 9 9 9 9 1,2,4 1,8 2,7 3,6 4,5 9
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..500
Crossrefs
Programs
-
Ruby
def A(n) f_ary = [[n]] cnt = 1 while f_ary.size > 0 b_ary = [] f_ary.each{|i| s = i.size (1..i[0] - 1).each{|j| a = [j] (0..s - 1).each{|k| num = i[k] - a[k] if num > 0 a << num else break end } b_ary << a if a.size == s + 1 && a == a.uniq.sort } } f_ary = b_ary cnt += f_ary.size end cnt end def A337766(n) (1..n).map{|i| A(i)} end p A337766(50)
Comments