A082793 A tribonacci triangle in which the top two northeast and southeast diagonals consist of tribonacci numbers.

1, 1, 1, 2, 1, 2, 4, 2, 2, 4, 7, 4, 4, 4, 7, 13, 7, 8, 8, 7, 13, 24, 13, 14, 16, 14, 13, 24, 44, 24, 26, 28, 28, 26, 24, 44

Offset: 1

Author

Gary W. Adamson, May 24 2003

Keywords

• nonn

Comments

Uses a Hosoya-like format except that the latter has the Fibonacci recursion. This triangle uses the tribonacci recursion such that every interior number can be obtained by adding the 3 previous numbers, on its diagonal.

Examples

			T(7,3) = 14 = (8 + 4 + 2) = T(6,3) + T(5,3) + T(4,3).
		

References

• Thomas Koshy, <"Fibonacci and Lucas Numbers with Applications">John Wiley and Sons, 2001, Chapter 15, pages 187-195, "Hosoya's Triangle".

Crossrefs

Cf. A000073, tribonacci numbers, A058071, Hosoya's triangle.

Formula

T(n, j) = T(n-1, j) + T(n-2, j) + T(n-3, j); (every interior number can be obtained by adding the three previous numbers, on its diagonal.)