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 A139701 Binomial transform of [1, 100, 100, 100, ...]. 7
 1, 101, 301, 701, 1501, 3101, 6301, 12701, 25501, 51101, 102301, 204701, 409501, 819101, 1638301, 3276701, 6553501, 13107101, 26214301, 52428701, 104857501, 209715101, 419430301, 838860701, 1677721501, 3355443101, 6710886301, 13421772701, 26843545501 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 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 A007318 * [1, 100, 100, 100, ...]. a(n) = 100*2^(n-1)-99. - Emeric Deutsch, May 03 2008 a(n) = 2*a(n-1)+99 for n > 1. [Vincenzo Librandi, Nov 24 2010] a(n) = 3*a(n-1) - 2*a(n-2) for n > 2. G.f.: x*(98*x+1) / ((x-1)*(2*x-1)). - Colin Barker, Mar 11 2014 EXAMPLE a(3) = 301 = (1, 2, 1) dot (1, 100, 100) = (1 + 200 + 100). MAPLE a:=proc(n) options operator, arrow: 100*2^(n-1)-99 end proc: seq(a(n), n=1.. 30); # Emeric Deutsch, May 03 2008 MATHEMATICA 100*2^(Range[30] - 1) - 99 (* Wesley Ivan Hurt, Aug 16 2016 *) LinearRecurrence[{3, -2}, {1, 101}, 40] (* Vincenzo Librandi, Aug 17 2016 *) PROG (PARI) Vec(x*(98*x+1)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Mar 11 2014 (MAGMA) [100*2^(n-1)-99 : n in [1..30]]; // Wesley Ivan Hurt, Aug 16 2016 CROSSREFS Cf. A007318, A099003, A139634, A139635, A139697, A139698, A139700, A139701. Sequence in context: A142530 A033241 A140021 * A195294 A142578 A256048 Adjacent sequences:  A139698 A139699 A139700 * A139702 A139703 A139704 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 January 17 10:21 EST 2022. Contains 350387 sequences. (Running on oeis4.)