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Search: id:A050613
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| A050613 |
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Products of distinct terms of 1 and rest from A001566: a(n) = Product(L(2^i)^bit(n,i),i=0..[log2(n+1)]). |
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6
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| 1, 1, 3, 3, 7, 7, 21, 21, 47, 47, 141, 141, 329, 329, 987, 987, 2207, 2207, 6621, 6621, 15449, 15449, 46347, 46347, 103729, 103729, 311187, 311187, 726103, 726103, 2178309, 2178309, 4870847, 4870847, 14612541, 14612541, 34095929, 34095929
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OFFSET
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0,3
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COMMENT
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Used to produce the rows of A050609.
Also Sum(((C(2((n+((n+1) mod 2)) mod (2^[log2(n)])),i) mod 2)*F(n+((n+1) mod 2)-i)),i=0..2((n+((n+1) mod 2)) mod (2^[log2(n)]))) or Sum(((C(2((n-(n mod 2)) mod (2^[log2(n)])),i) mod 2)*L(n-(n mod 2)-i)),i=0..2((n-(n mod 2)) mod (2^[log2(n)]))) for all n > 1. Here F(n) and L(n) are n-th Fibonacci (A000045) and Lucas (A000032) numbers respectively.
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LINKS
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A. Karttunen, On Pascal's Triangle Modulo 2 in Fibonacci Representation, Fibonacci Quarterly, 42 (2004), 38-46.
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MAPLE
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with(combinat); A050613 := n -> product('luc(2^i)^bit_i(n, i)', 'i'=0..floor_log_2(n+1));
luc := n -> (fibonacci(n-1)+fibonacci(n+1));
bit_i := (n, i) -> `mod`(floor(n/(2^i)), 2);
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;
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CROSSREFS
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Bisection: A050614.
Sequence in context: A147236 A146599 A107222 this_sequence A145940 A147103 A003133
Adjacent sequences: A050610 A050611 A050612 this_sequence A050614 A050615 A050616
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen Dec 02 1999
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