230430

Ruby


A275216

q-binomialの係数を出力してみた。

def plus(f_ary, b_ary)
  s1, s2 = f_ary.size, b_ary.size
  ary = Array.new([s1, s2].max, 0)
  (0..s1 - 1).each{|i| ary[i] += f_ary[i]}
  (0..s2 - 1).each{|i| ary[i] += b_ary[i]}
  ary
end

def A(n)
  ary = [[1]]
  a = [[[1]]]
  (1..n).each{|i|
    new_ary = [[0]] + ary
    (0..i - 1).each{|j| 
      new_ary[j] = plus(new_ary[j], [0] * j + ary[j])
    }
    ary = new_ary
    a << ary
  }
  a
end

n = 10
A(n).each_with_index{|i, num|
  puts "Row #{num}"
  i.each{|j| p j}
}

出力結果

Row 0

[1]

Row 1

[1]

[1]

Row 2

[1]

[1, 1]

[1]

Row 3

[1]

[1, 1, 1]

[1, 1, 1]

[1]

Row 4

[1]

[1, 1, 1, 1]

[1, 1, 2, 1, 1]

[1, 1, 1, 1]

[1]

Row 5

[1]

[1, 1, 1, 1, 1]

[1, 1, 2, 2, 2, 1, 1]

[1, 1, 2, 2, 2, 1, 1]

[1, 1, 1, 1, 1]

[1]

Row 6

[1]

[1, 1, 1, 1, 1, 1]

[1, 1, 2, 2, 3, 2, 2, 1, 1]

[1, 1, 2, 3, 3, 3, 3, 2, 1, 1]

[1, 1, 2, 2, 3, 2, 2, 1, 1]

[1, 1, 1, 1, 1, 1]

[1]

Row 7

[1]

[1, 1, 1, 1, 1, 1, 1]

[1, 1, 2, 2, 3, 3, 3, 2, 2, 1, 1]

[1, 1, 2, 3, 4, 4, 5, 4, 4, 3, 2, 1, 1]

[1, 1, 2, 3, 4, 4, 5, 4, 4, 3, 2, 1, 1]

[1, 1, 2, 2, 3, 3, 3, 2, 2, 1, 1]

[1, 1, 1, 1, 1, 1, 1]

[1]

Row 8

[1]

[1, 1, 1, 1, 1, 1, 1, 1]

[1, 1, 2, 2, 3, 3, 4, 3, 3, 2, 2, 1, 1]

[1, 1, 2, 3, 4, 5, 6, 6, 6, 6, 5, 4, 3, 2, 1, 1]

[1, 1, 2, 3, 5, 5, 7, 7, 8, 7, 7, 5, 5, 3, 2, 1, 1]

[1, 1, 2, 3, 4, 5, 6, 6, 6, 6, 5, 4, 3, 2, 1, 1]

[1, 1, 2, 2, 3, 3, 4, 3, 3, 2, 2, 1, 1]

[1, 1, 1, 1, 1, 1, 1, 1]

[1]

Row 9

[1]

[1, 1, 1, 1, 1, 1, 1, 1, 1]

[1, 1, 2, 2, 3, 3, 4, 4, 4, 3, 3, 2, 2, 1, 1]

[1, 1, 2, 3, 4, 5, 7, 7, 8, 8, 8, 7, 7, 5, 4, 3, 2, 1, 1]

[1, 1, 2, 3, 5, 6, 8, 9, 11, 11, 12, 11, 11, 9, 8, 6, 5, 3, 2, 1, 1]

[1, 1, 2, 3, 5, 6, 8, 9, 11, 11, 12, 11, 11, 9, 8, 6, 5, 3, 2, 1, 1]

[1, 1, 2, 3, 4, 5, 7, 7, 8, 8, 8, 7, 7, 5, 4, 3, 2, 1, 1]

[1, 1, 2, 2, 3, 3, 4, 4, 4, 3, 3, 2, 2, 1, 1]

[1, 1, 1, 1, 1, 1, 1, 1, 1]

[1]

Row 10

[1]

[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

[1, 1, 2, 2, 3, 3, 4, 4, 5, 4, 4, 3, 3, 2, 2, 1, 1]

[1, 1, 2, 3, 4, 5, 7, 8, 9, 10, 10, 10, 10, 9, 8, 7, 5, 4, 3, 2, 1, 1]

[1, 1, 2, 3, 5, 6, 9, 10, 13, 14, 16, 16, 18, 16, 16, 14, 13, 10, 9, 6, 5, 3, 2, 1, 1]

[1, 1, 2, 3, 5, 7, 9, 11, 14, 16, 18, 19, 20, 20, 19, 18, 16, 14, 11, 9, 7, 5, 3, 2, 1, 1]

[1, 1, 2, 3, 5, 6, 9, 10, 13, 14, 16, 16, 18, 16, 16, 14, 13, 10, 9, 6, 5, 3, 2, 1, 1]

[1, 1, 2, 3, 4, 5, 7, 8, 9, 10, 10, 10, 10, 9, 8, 7, 5, 4, 3, 2, 1, 1]

[1, 1, 2, 2, 3, 3, 4, 4, 5, 4, 4, 3, 3, 2, 2, 1, 1]

[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

[1]