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 A139635 Binomial transform of [1, 11, 11, 11,...]. 7
 1, 12, 34, 78, 166, 342, 694, 1398, 2806, 5622, 11254, 22518, 45046, 90102, 180214, 360438, 720886, 1441782, 2883574, 5767158, 11534326, 23068662, 46137334, 92274678, 184549366, 369098742, 738197494, 1476394998, 2952790006, 5905580022, 11811160054 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A007318 * [1, 11, 11, 11,...]. The binomial transform of [1, c, c, c,...] has the terms a(n)=1-c+c*2^(n-1) if the offset 1 is chosen. The o.g.f. of the a(n) is x{1+(c-2)x}/{(2x-1)(x-1)}. This applies to A139634 with c=10, to A139635 with c=11, to A139697 with c=12, to A139698 with c=25 and to A099003, A139700, A139701 accordingly. - R. J. Mathar, May 11 2008 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (3,-2). FORMULA a(n) = 11*2^(n-1)-10. - Emeric Deutsch, May 03 2008 a(n) = 2*a(n-1)+10, with n>1, a(1)=1. - Vincenzo Librandi, Nov 24 2010] a(n) = 3*a(n-1)-2*a(n-2). G.f.: x*(9*x+1) / ((x-1)*(2*x-1)). - Colin Barker, Mar 11 2014 EXAMPLE a(4) = 78 = (1, 3, 3, 1) dot (1, 11, 11, 11) = (1 + 33 + 33 + 11). MAPLE seq(11*2^(n-1)-10, n=1.. 25); # Emeric Deutsch, May 03 2008 MATHEMATICA a=1; lst={a}; k=11; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 17 2008 *) CoefficientList[Series[(9 x + 1)/((x - 1) (2 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 13 2014 *) LinearRecurrence[{3, -2}, {1, 12}, 40] (* Harvey P. Dale, Oct 26 2015 *) PROG (PARI) Vec(x*(9*x+1)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Mar 11 2014 CROSSREFS Cf. A139634. Sequence in context: A113748 A069125 A142245 * A124705 A296154 A126366 Adjacent sequences:  A139632 A139633 A139634 * A139636 A139637 A139638 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Apr 29 2008 EXTENSIONS More terms from Emeric Deutsch, May 03 2008 More terms from Colin Barker, Mar 11 2014 STATUS approved

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Last modified June 18 20:43 EDT 2021. Contains 345121 sequences. (Running on oeis4.)