A075148 Table E(n,k) (listed antidiagonalwise as E(0,0), E(1,0), E(0,1), E(2,0), E(1,1), E(0,2), ...) where E(n,k) is F(n+k) for all even n and L(n+k) for all odd n. F(n) and L(n) are the n-th Fibonacci (A000045) and Lucas (A000032) numbers respectively.

0, 1, 1, 1, 3, 1, 4, 2, 4, 2, 3, 7, 3, 7, 3, 11, 5, 11, 5, 11, 5, 8, 18, 8, 18, 8, 18, 8, 29, 13, 29, 13, 29, 13, 29, 13, 21, 47, 21, 47, 21, 47, 21, 47, 21, 76, 34, 76, 34, 76, 34, 76, 34, 76, 34, 55, 123, 55, 123, 55, 123, 55, 123, 55, 123, 55, 199, 89, 199, 89, 199, 89, 199

Offset: 0

Author

Antti Karttunen, Sep 05 2002

Keywords

• nonn
• tabl

Crossrefs

Used to construct A050609 & A048757. Cf. A025581, A002262.

Programs

Maple

with(combinat); [seq(A075148(A025581(n), A002262(n)),n=0..119)]; A075148 := (n,k) -> (fibonacci(n+k-(n mod 2))+fibonacci(n+k+(n mod 2)))/(2-(n mod 2));

Formula

E(n, k) = (fibonacci(n+k-(n mod 2))+fibonacci(n+k+(n mod 2)))/(2-(n mod 2))