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A129707
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Number of inversions in all Fibonacci binary words of length n. A Fibonacci binary word is a binary word having no 00 subword.
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4
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0, 0, 1, 4, 12, 31, 73, 162, 344, 707, 1416, 2778, 5358, 10188, 19139, 35582, 65556, 119825, 217487, 392286, 703618, 1255669, 2230608, 3946020, 6954060, 12212280, 21377365, 37309288, 64935132, 112726771, 195224773, 337343034, 581700476
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| a(n)=Sum(k*A129706(n,k), k>=0).
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,0,-5,0,3,1).
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FORMULA
| G.f.=z^2*(1+z)/(1-z-z^2)^3. Rec. rel:= a(n)=2a(n-1)+a(n-2)-2a(n-3)-a(n-4)+F(n), a(0)=a(1)=0,a(2)=1,a(3)=4
a(n-3) = ((5n^2-37n+50)*F(n-1) + 4(n-1)*F(n))/50 = (-1)^n*A055243(-n). - Peter Bala (pbala(AT)toucansurf.com), Oct 25 2007
a(n) = A001628(n-3)+A001628(n-2). - R. J. Mathar, Dec 07 2011
a(n+1) = A123585(n+2,n). - DELEHAM Philippe, Dec 18 2011
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EXAMPLE
| a(3)=4 because the Fibonacci words 110,111,101,010,011 have a total of 2+0+1+1+0 = 4 inversions.
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MAPLE
| with(combinat): a[0]:=0: a[1]:=0: a[2]:=1: a[3]:=4: for n from 4 to 40 do a[n]:=2*a[n-1]+a[n-2]-2*a[n-3]-a[n-4]+fibonacci(n) od: seq(a[n], n=0..40);
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CROSSREFS
| Cf. A129706.
Cf. A055243.
Sequence in context: A037255 A027658 A001982 * A133546 A190376 A171844
Adjacent sequences: A129704 A129705 A129706 * A129708 A129709 A129710
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), May 12 2007
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