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%I #22 Sep 08 2022 08:45:33
%S 1,101,301,701,1501,3101,6301,12701,25501,51101,102301,204701,409501,
%T 819101,1638301,3276701,6553501,13107101,26214301,52428701,104857501,
%U 209715101,419430301,838860701,1677721501,3355443101,6710886301,13421772701,26843545501
%N Binomial transform of [1, 100, 100, 100, ...].
%C 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
%H Vincenzo Librandi, <a href="/A139701/b139701.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A007318 * [1, 100, 100, 100, ...].
%F a(n) = 100*2^(n-1)-99. - _Emeric Deutsch_, May 03 2008
%F a(n) = 2*a(n-1)+99 for n > 1. [_Vincenzo Librandi_, Nov 24 2010]
%F 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
%e a(3) = 301 = (1, 2, 1) dot (1, 100, 100) = (1 + 200 + 100).
%p a:=proc(n) options operator, arrow: 100*2^(n-1)-99 end proc: seq(a(n), n=1.. 30); # _Emeric Deutsch_, May 03 2008
%t 100*2^(Range[30] - 1) - 99 (* _Wesley Ivan Hurt_, Aug 16 2016 *)
%t LinearRecurrence[{3, -2}, {1, 101}, 40] (* _Vincenzo Librandi_, Aug 17 2016 *)
%o (PARI) Vec(x*(98*x+1)/((x-1)*(2*x-1)) + O(x^100)) \\ _Colin Barker_, Mar 11 2014
%o (Magma) [100*2^(n-1)-99 : n in [1..30]]; // _Wesley Ivan Hurt_, Aug 16 2016
%Y Cf. A007318, A099003, A139634, A139635, A139697, A139698, A139700, A139701.
%K nonn,easy
%O 1,2
%A _Gary W. Adamson_, Apr 29 2008
%E More terms from _Emeric Deutsch_, May 03 2008
%E More terms from _Colin Barker_, Mar 11 2014