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A140065
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(7n^2 - 17n + 12)/2.
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0
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1, 3, 12, 28, 51, 81, 118, 162, 213, 271, 336, 408, 487, 573, 666, 766, 873, 987, 1108, 1236, 1371, 1513, 1662, 1818, 1981, 2151, 2328, 2512, 2703, 2901, 3106, 3318, 3537, 3763, 3996, 4236, 4483, 4737, 4998, 5266, 5541, 5823, 6112, 6408, 6711, 7021, 7338
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OFFSET
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1,2
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COMMENTS
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Binomial transform of [1, 2, 7, 0, 0, 0,...].
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LINKS
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Table of n, a(n) for n=1..47.
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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A007318 * [1, 2, 7, 0, 0, 0,...]
a(n) = A000217(n)+6*A000217(n-2) = (A140064(n)+A140066(n))/2. O.g.f.: x*(1+6x^2)/(1-x)^3. - R. J. Mathar, May 06 2008
Ogf([1,3,12,28,51,81,118,162,213,271,336,408,487,573]) = (6*x^2 + 1)/(-x^3 + 3*x^2 - 3*x + 1) - Alexander R. Povolotsky, May 06 2008
a(n)=7*n+a(n-1)-12 (with a(1)=1) [From Vincenzo Librandi, Jul 08 2010]
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EXAMPLE
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a(4) = 28 = (1, 3, 3, 1) dot (1, 2, 7, 0) = (1 + 6 + 21 + 0).
For n=2, a(2)=7*2+1-12=3; n=3, a(3)=7*3+3-12=12; n=4, a(4)=7*4+12-12=28 [From Vincenzo Librandi, Jul 08 2010]
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MAPLE
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seq((12-17*n+7*n^2)*1/2, n=1..40); - Emeric Deutsch, May 07 2008
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MATHEMATICA
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s=1; lst={s}; Do[s+=n+1; AppendTo[lst, s], {n, 1, 6!, 7}]; lst [From Vladimir Joseph Stephan Orlovsky, Oct 25 2008]
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CROSSREFS
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Sequence in context: A060781 A083539 A066643 * A115549 A005995 A034503
Adjacent sequences: A140062 A140063 A140064 * A140066 A140067 A140068
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KEYWORD
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nonn,easy
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AUTHOR
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Gary W. Adamson, May 03 2008
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EXTENSIONS
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More terms from R. J. Mathar and Emeric Deutsch, May 06 2008
More terms and Mathematica program Vladimir Joseph Stephan Orlovsky, Oct 25 2008
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STATUS
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approved
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