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Fibonacci triangle or the Hosoya's triangle is a triangular arrangement of numbers (like Pascal's triangle) based on the Fibonacci numbers. Each number is the sum of the two numbers above in either the left diagonal or the right diagonal. The first few rows are: 1 1 1 2 1 2 3 2 2 3 5 3 4 3 5 8 5 6 6 5 8 13 8 10 9 10 8 13 21 13 16 15 15 16 13 21 34 21 26 24 25 24 26 21 34 55 34 42 39 40 40 39 42 34 55 89 55 68 63 65 64 65 63 68 55 89 144 89 110 102 105 104 104 105 102 110 89 144 etc. (See ). The recurrence relation is ''H''(0, 0) = ''H''(1, 0) = ''H''(1, 1) = ''H''(2, 1) = 1 and ''H''(''n'', ''j'') = ''H''(''n'' − 1, ''j'') + ''H''(''n'' − 2, ''j'') or ''H''(''n'', ''j'') = ''H''(''n'' − 1, ''j'' − 1) + ''H''(''n'' − 2, ''j'' − 2). The entries in the triangle satisfy the identity :''H''(''n'', ''i'') = ''F''(''i'' + 1) × ''F''(''n'' − ''i'' + 1). Thus, the two outermost diagonals are the Fibonacci numbers, while the numbers on the middle vertical line are the squares of the Fibonacci numbers. All the other numbers in the triangle are the product of two distinct Fibonacci numbers greater than 1. The row sums are the first convolved Fibonacci numbers. ==References== * Haruo Hosoya, "Fibonacci Triangle" ''The Fibonacci Quarterly'' 14 2 (1976): 173–178 * Thomas Koshy, ''Fibonacci and Lucas Numbers and Applications''. New York: Wiley & Sons (2001): 187–195 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hosoya's triangle」の詳細全文を読む スポンサード リンク
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