OFFSET
0,2
COMMENTS
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).
LINKS
Antti Karttunen, On Pascal's Triangle Modulo 2 in Fibonacci Representation, Fibonacci Quarterly, 42 (2004), 38-46.
EXAMPLE
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.
MATHEMATICA
Table[Sum[Mod[Binomial[2n, i], 2] Fibonacci[i + 2], {i, 0, 2n}], {n, 0, 19}] (* Alonso del Arte, Apr 27 2014 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Antti Karttunen, Jul 13 1999
STATUS
approved