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A140065
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a(n) = (7*n^2 - 17*n + 12)/2.
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1
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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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G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for 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. - R. J. Mathar, May 06 2008
o.g.f.: x*(1+6*x^2)/(1-x)^3. - Alexander R. Povolotsky, May 06 2008
a(n) = 7*n + a(n-1) - 12 for n>1, a(1)=1. - Vincenzo Librandi, Jul 08 2010
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EXAMPLE
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a(4) = 28 = (1, 3, 3, 1) * (1, 2, 7, 0) = (1 + 6 + 21 + 0).
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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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Table[(7 n^2 - 17 n + 12)/2, {n, 1, 50}] (* Bruno Berselli, Mar 12 2015 *)
LinearRecurrence[{3, -3, 1}, {1, 3, 12}, 50] (* Harvey P. Dale, May 28 2017 *)
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PROG
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(PARI) x = 'x + O('x^50); Vec(x*(1+6*x^2)/(1-x)^3) \\ G. C. Greubel, Feb 23 2017
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CROSSREFS
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Cf. A000217.
Sequence in context: A083539 A237426 A066643 * A294418 A115549 A005995
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 from Vladimir Joseph Stephan Orlovsky, Oct 25 2008
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STATUS
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approved
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