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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.
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%I #5 May 01 2014 02:48:30

%S 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,

%T 29,13,29,13,29,13,21,47,21,47,21,47,21,47,21,76,34,76,34,76,34,76,34,

%U 76,34,55,123,55,123,55,123,55,123,55,123,55,199,89,199,89,199,89,199

%N 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.

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

%p 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));

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

%K nonn,tabl

%O 0,5

%A _Antti Karttunen_, Sep 05 2002