A075149 Sum_{i=0..2*A053645(n)} (C(2*A053645(n),i) mod 2)*A000045(n-i) [where C(r,c) is the binomial coefficient (A007318) and A000045(n) is the n-th Fibonacci number].

0, 1, 1, 3, 3, 7, 9, 21, 21, 47, 63, 141, 147, 329, 441, 987, 987, 2207, 2961, 6621, 6909, 15449, 20727, 46347, 46389, 103729, 139167, 311187, 324723, 726103, 974169, 2178309, 2178309, 4870847, 6534927, 14612541, 15248163, 34095929, 45744489

Offset

0,4

Links

Table of n, a(n) for n=0..38.

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

Maple

with(combinat): r := n -> n - 2^floor_log_2(n): floor_log_2 := proc(n) local nn, i; nn := n; for i from -1 to n do if 0 = nn then return i; fi; nn := floor(nn/2); od; end:
A075149 := n -> add((binomial(2*r(n), i) mod 2)*fibonacci(n-i), i=0..2*r(n)):
seq(A075149(n), n=0..50);

Crossrefs

Bisection gives A050614.

Sequence in context: A320314 A056295 A117525 * A161618 A202873 A157933

Adjacent sequences: A075146 A075147 A075148 * A075150 A075151 A075152

Keyword

nonn

Author

Antti Karttunen, Sep 05 2002

Status

approved