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 A139634 10*2^(n-1) - 9. 9
 1, 11, 31, 71, 151, 311, 631, 1271, 2551, 5111, 10231, 20471, 40951, 81911, 163831, 327671, 655351, 1310711, 2621431, 5242871, 10485751, 20971511, 41943031, 83886071, 167772151, 335544311, 671088631, 1342177271, 2684354551 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Binomial transform of [1, 10, 10, 10,...]. A007318 * [1, 10, 10, 10,...]. 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) = 2*a(n-1) + 9, with n>1, a(1)=1. - Vincenzo Librandi, Nov 24 2010 a(n) = 3*a(n-1) - 2*a(n-2). G.f.: x*(8*x+1) / ((x-1)*(2*x-1)). - Colin Barker, Oct 10 2013 EXAMPLE a(4) = 71 = (1, 3, 3, 1) dot (1, 10, 10, 10) = (1 + 30 + 30 + 10). MAPLE A139634:=n->10*2^(n-1)-9; seq(A139634(n), n=1..30); # Wesley Ivan Hurt, Mar 26 2014 MATHEMATICA a=1; lst={a}; k=10; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 17 2008 *) CoefficientList[Series[(8 x + 1)/((x - 1) (2 x - 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 30 2014 *) PROG (MAGMA) [10*2^(n-1)-9: n in [1..50]]; // Vincenzo Librandi, Mar 30 2014 (PARI) a(n)=10*2^(n-1)-9 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Sequence in context: A085715 A040973 A141884 * A173803 A124704 A293659 Adjacent sequences:  A139631 A139632 A139633 * A139635 A139636 A139637 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Apr 29 2008 EXTENSIONS More terms from Vladimir Joseph Stephan Orlovsky, Dec 17 2008 Simpler definition from Jon E. Schoenfield, Jun 23 2010 STATUS approved

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Last modified October 24 12:42 EDT 2021. Contains 348231 sequences. (Running on oeis4.)