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A152881
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Positions of those 1's that are followed by a 0, summed over all Fibonacci binary words of length n. A Fibonacci binary word is a binary word having no 00 subword.
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0
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0, 1, 5, 15, 40, 95, 213, 455, 940, 1890, 3720, 7194, 13710, 25805, 48055, 88665, 162272, 294865, 532395, 955795, 1707110, 3034836, 5372400, 9473700, 16646700, 29155225, 50908793, 88644915, 153952120, 266726195, 461066385, 795320159
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n)=Sum(k*A119469(n+1,k),k>=0).
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FORMULA
| G.f. = z^2*(1+2z)/(1-z-z^2)^3.
a(n)=A001628(n-1)+2*A001628(n-2), n>1, a(0)=0, a(1)=1. [From Vladimir Kruchinin kru(AT)ie.tusur.ru, Apr 26 2011]
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EXAMPLE
| a(4)=15 because the Fibonacci binary words of length 4 are 1110, 1111, 1101, 1010, 1011, 0110, 0111, 0101 and the positions of those 1's that are followed by a 0 are 3, 2, 1, 3, 1, 3 and 2; their sum is 15.
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MAPLE
| G := z^2*(1+2*z)/(1-z-z^2)^3: Gser := series(G, z = 0, 38): seq(coeff(Gser, z, n), n = 1 .. 34);
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CROSSREFS
| A119469
Sequence in context: A034182 A132985 A022570 * A000333 A201157 A054888
Adjacent sequences: A152878 A152879 A152880 * A152882 A152883 A152884
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 04 2009
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