A337787 Number of addition triangles whose sum is n (version 2).
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, 4, 16, 9, 14, 7, 20, 8, 18, 11, 20, 12, 25, 8, 25, 18, 24, 12, 31, 16, 32, 19, 29, 21, 39, 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
Offset: 1
Examples
n |
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1 | 1
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2 | 2
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3 | 3
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4 | 2
| 4 1,1
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5 | 5
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6 | 3
| 6 1,2
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7 | 7
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8 | 4 4
| 8 1,3 2,2
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9 | 9
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10 | 5 5
| 10 1,4 2,3
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11 | 4
| 2,2
| 11 1,1,1
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12 | 6 6 6
| 12 1,5 2,4 3,3
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13 | 13
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14 | 5
| 7 7 7 2,3
| 14 1,6 2,5 3,4 1,1,2
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15 | 15
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16 | 6
| 8 8 8 8 3,3
| 16 1,7 2,6 3,5 4,4 1,2,1
-----+-------------------------------
17 | 6 6
| 2,4 3,3
| 17 1,1,3 2,1,2
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18 | 9 9 9 9
| 18 1,8 2,7 3,6 4,5
-----+-------------------------------
19 | 7
| 3,4
| 19 1,2,2
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..500
Programs
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Ruby
def f(n) ary = [1] (n - 1).times{|i| ary = [0] + ary + [0] ary = (0..i + 1).map{|j| ary[j] + ary[j + 1] + 1} } ary end def A(n) f_ary = (1..n / 2).map{|i| [i]} cnt = 2 s = 1 while f_ary.size > 0 s_ary = f(s + 1) b_ary = [] f_ary.each{|i| (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 } if a.size == s + 1 sum = (0..s).inject(0){|t, m| t + s_ary[m] * a[m]} if sum < n b_ary << a elsif sum == n cnt += 1 cnt += 1 if a == a.reverse end end } } f_ary = b_ary s += 1 end cnt / 2 end def A337787(n) (1..n).map{|i| A(i)} end p A337787(50)
Comments