A050609 Table T(n,k) = Sum_{i=0..2n} (C(2n,i) mod 2)*F(i+k) = Sum_{i=0..n} (C(n,i) mod 2)*F(2i+k).

0, 1, 1, 3, 3, 1, 12, 6, 4, 2, 21, 21, 9, 7, 3, 77, 35, 33, 15, 11, 5, 168, 126, 56, 54, 24, 18, 8, 609, 273, 203, 91, 87, 39, 29, 13, 987, 987, 441, 329, 147, 141, 63, 47, 21, 3572, 1598, 1596, 714, 532, 238, 228, 102, 76, 34, 7755, 5781, 2585, 2583, 1155, 861, 385

Offset: 0

Author

Antti Karttunen, Dec 02 1999

Keywords

• nonn
• tabl

Comments

Listed antidiagonalwise as T(0,0), T(1,0), T(0,1), T(2,0), T(1,1), T(0,2), ...

Links

• A. Karttunen, On Pascal's Triangle Modulo 2 in Fibonacci Representation, Fibonacci Quarterly, 42 (2004), 38-46.

Crossrefs

Transpose of A050610. First row: A051656, second row: A050611, third row: A048757, fourth row: A050612. A050613 gives other Maple procedures. Cf. A025581, A002262.

Programs

Maple

A050609_as_sum := proc(n,k) local i; RETURN(add(((binomial(n,i) mod 2)*fibonacci(k+2*i)),i=0..n)); end;
A050609_as_product := (n,k) -> (`if`(1 = (n mod 2),luc(n+k),fibonacci(n+k)))*product('luc(2^i)^bit_i(n,i)','i'=1..floor_log_2(n+1)); # Produces same answers.
[seq(A050609_as_sum(A025581(n), A002262(n)),n=0..119)];

Formula

Also a(n) = A075148(n, k)*A050613(n).