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 A140065 a(n) = (7*n^2 - 17*n + 12)/2. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Binomial transform of [1, 2, 7, 0, 0, 0,...]. LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA 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 EXAMPLE a(4) = 28 = (1, 3, 3, 1) * (1, 2, 7, 0) = (1 + 6 + 21 + 0). MAPLE seq((12-17*n+7*n^2)*1/2, n=1..40); # Emeric Deutsch, May 07 2008 MATHEMATICA 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 *) PROG (PARI) x = 'x + O('x^50); Vec(x*(1+6*x^2)/(1-x)^3) \\ G. C. Greubel, Feb 23 2017 CROSSREFS Cf. A000217. Sequence in context: A083539 A237426 A066643 * A294418 A308669 A115549 Adjacent sequences:  A140062 A140063 A140064 * A140066 A140067 A140068 KEYWORD nonn,easy AUTHOR Gary W. Adamson, May 03 2008 EXTENSIONS More terms from R. J. Mathar and Emeric Deutsch, May 06 2008 More terms from Vladimir Joseph Stephan Orlovsky, Oct 25 2008 STATUS approved

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Last modified April 18 10:21 EDT 2021. Contains 343087 sequences. (Running on oeis4.)