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A059502
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a(n) = (3*n*F(2n-1) + (3-n)*F(2n))/5 where F() = Fibonacci numbers A000045.
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11
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0, 1, 3, 9, 27, 80, 234, 677, 1941, 5523, 15615, 43906, 122868, 342409, 950727, 2631165, 7260579, 19982612, 54865566, 150316973, 411015705, 1121818311, 3056773383, 8316416134, 22593883752, 61301547025, 166118284299, 449639574897, 1215751720491, 3283883157848
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OFFSET
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0,3
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COMMENTS
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Substituting x(1-x)/(1-2x) into x/(1-x)^2 yields g.f. of sequence.
Variation of A059216 (and of Boustrophedon transform) applied to 1,2,3,4,...: fill an array by diagonals, each time in the same direction, say the 'up' direction. The first column is 1,2,3,4,... For the next element of a diagonal, add to the previous element the elements of the row the new element is in. The first row gives a(n).
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LINKS
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FORMULA
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a(n) = 2*a(n-1) + Sum{m<=n-2}a(m) + A001519(n-2).
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EXAMPLE
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1 3 9 27 80 ...
2 5 14 40 ...
3 7 19 ...
4 9 5 ...
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MATHEMATICA
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Table[(3n Fibonacci[2n-1]+(3-n)Fibonacci[2n])/5, {n, 0, 30}] (* or *) CoefficientList[Series[x(1-x)(1-2x)/(1-3x+x^2)^2, {x, 0, 30}], x] (* Harvey P. Dale, Apr 23 2011 *)
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PROG
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(PARI) a(n)=(3*n*fibonacci(2*n-1)+(3-n)*fibonacci(2*n))/5
(PARI) { for (n = 0, 200, write("b059502.txt", n, " ", (3*n*fibonacci(2*n - 1) + (3 - n)*fibonacci(2*n))/5); ) } \\ Harry J. Smith, Jun 27 2009
(Magma) [(3*n*Fibonacci(2*n-1)+(3-n)*Fibonacci(2*n))/5: n in [0..100]]; // Vincenzo Librandi, Apr 23 2011
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CROSSREFS
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KEYWORD
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easy,nonn,nice
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AUTHOR
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STATUS
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approved
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