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- Hosoya's_triangle abstract "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(See (sequence A058071 in OEIS)). 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 identityH(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.".
- Hosoya's_triangle wikiPageID "17813366".
- Hosoya's_triangle wikiPageRevisionID "565803041".
- Hosoya's_triangle hasPhotoCollection Hosoya's_triangle.
- Hosoya's_triangle subject Category:Fibonacci_numbers.
- Hosoya's_triangle subject Category:Triangles_of_numbers.
- Hosoya's_triangle type Abstraction100002137.
- Hosoya's_triangle type Amount105107765.
- Hosoya's_triangle type Attribute100024264.
- Hosoya's_triangle type FibonacciNumbers.
- Hosoya's_triangle type Figure113862780.
- Hosoya's_triangle type Magnitude105090441.
- Hosoya's_triangle type Number105121418.
- Hosoya's_triangle type PlaneFigure113863186.
- Hosoya's_triangle type Polygon113866144.
- Hosoya's_triangle type Property104916342.
- Hosoya's_triangle type Shape100027807.
- Hosoya's_triangle type Triangle113879320.
- Hosoya's_triangle type TrianglesOfNumbers.
- Hosoya's_triangle comment "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.".
- Hosoya's_triangle label "Hosoya's triangle".
- Hosoya's_triangle sameAs m.0479gw0.
- Hosoya's_triangle sameAs Q17027607.
- Hosoya's_triangle sameAs Q17027607.
- Hosoya's_triangle sameAs Hosoya's_triangle.
- Hosoya's_triangle wasDerivedFrom Hosoya's_triangle?oldid=565803041.
- Hosoya's_triangle isPrimaryTopicOf Hosoya's_triangle.