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A059502
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(3*n*F(2n-1)+(3-n)*F(2n))/5 where F() = Fibonacci numbers A000045.
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10
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
| Harry J. Smith, Table of n, a(n) for n=0,...,200
Index entries for two-way infinite sequences
Index entries for sequences related to boustrophedon transform
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FORMULA
| a(n) = 2*a(n-1) + Sum{m<=n-2}a(m) + A001519(n-2).
G.f.= x(1-x)(1-2x)/(1-3x+x^2)^2. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 07 2002
a(n)=A147703(n,1). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 29 2008]
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EXAMPLE
| The array (see A059503) begins
1 3 9 27 80 ...
2 5 14 40 ...
3 7 19 ...
4 9 5 ...
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MATHEMATICA
| 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] (* From Harvey P. Dale, Apr 23 2011 *)
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PROG
| (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); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 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
| Cf. A000667, A059216, A059219, A027994, A059512, A059503.
Sequence in context: A077827 A129770 A134396 * A036142 A036160 A001218
Adjacent sequences: A059499 A059500 A059501 * A059503 A059504 A059505
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Floor van Lamoen (fvlamoen(AT)hotmail.com), Jan 19 2001
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