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Search: id:A048757
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| A048757 |
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Sum_{i=0..2n} (C(2n,i) mod 2)*Fibonacci(i+2) = Sum_{i=0..n} (C(n,i) mod 2)*Fibonacci(2i+2). |
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14
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| 1, 4, 9, 33, 56, 203, 441, 1596, 2585, 9353, 20304, 73461, 124033, 448756, 974169, 3524577, 5702888, 20633243, 44791065, 162055596, 273617239, 989956471, 2149017696, 7775219067, 12591974497, 45558191716, 98898651657
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The history of 1-D CA rule 90 starting from the seed pattern 1 interpreted as Zeckendorffian expansion.
Also, product of distinct terms of A001566 and appropriate Fibonacci or Lucas numbers: a(n) = FL(n+2)Product(L(2^i)^bit(n,i),i=0..) Here L(2^i) = A001566 and FL(n) = n-th Fibonacci number if n even, n-th Lucas number if n odd. bit(n,i) is the i-th digit (0 or 1) in the binary expansion of n, with the least significant digit being bit(n,0).
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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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EXAMPLE
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1 = Fib(2) = 1; 101 = Fib(4)+Fib(2) = 3+1 = 4; 10001 = Fib(6)+Fib(2) = 8+1 = 9; 1010101 = Fib(8)+Fib(6)+Fib(4)+Fib(2) = 21+8+3+1 = 33; etc...
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CROSSREFS
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a(n) = A022290(A038183(n)) = A022290(A048723(5, n)) = A003622(A051656(n)) = A075148(n, 2)*A050613(n). Third row of A050609, third column of A050610.
Cf. A054433.
Adjacent sequences: A048754 A048755 A048756 this_sequence A048758 A048759 A048760
Sequence in context: A119574 A006393 A076966 this_sequence A054433 A096531 A006392
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KEYWORD
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easy,nonn
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AUTHOR
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Antti Karttunen (my_firstname.my_surname), Jul 13 1999
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