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Search: id:A067988
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| 1, 3, 10, 25, 60, 133, 284, 585, 1175, 2310, 4464, 8502, 15995, 29775, 54920, 100487, 182556, 329555, 591550, 1056405, 1877821, 3323868, 5860800, 10297500, 18033925, 31487643, 54824854, 95211205, 164948700
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) is the sum of the positions of the 0's in all Fibonacci binary words of length n+1. A Fibonacci binary word is a binary word having no 00 subword. Example: a(3)=25 because the Fibonacci binary words of length 4 are 1110, 1111, 1101, 1010, 1011, 0110, 0111 and 0101, the positions of the 0's being 4, 3, 2, 4, 2, 1, 4, 1, 1 and 3 (their sum is 25). [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 04 2009]
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FORMULA
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a(n)= (n+2)*((3*n+5)*F(n+1)+(n+1)*F(n))/10, with F(n) := A000045(n) (Fibonacci).
G.f.: (1+x^2)/(1-x-x^2)^3.
Sum(binomial(n-j,j)*n*j/2,j=0..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 19 2006
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MAPLE
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a:=n->sum(binomial(n-j, j)*n*j/2, j=0..n): seq(a(n), n=2..30); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 19 2006
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CROSSREFS
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Cf. A001628.
Sequence in context: A000247 A097763 A034506 this_sequence A005674 A089100 A089117
Adjacent sequences: A067985 A067986 A067987 this_sequence A067989 A067990 A067991
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Feb 15 2002
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