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A139698 Binomial transform of [1, 25, 25, 25, ...].

%I A139698 #28 Sep 08 2022 08:45:33
%S A139698 1,26,76,176,376,776,1576,3176,6376,12776,25576,51176,102376,204776,
%T A139698 409576,819176,1638376,3276776,6553576,13107176,26214376,52428776,
%U A139698 104857576,209715176,419430376,838860776,1677721576,3355443176,6710886376,13421772776,26843545576
%N A139698 Binomial transform of [1, 25, 25, 25, ...].
%C A139698 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
%H A139698 Harvey P. Dale, <a href="/A139698/b139698.txt">Table of n, a(n) for n = 1..1000</a>
%H A139698 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A139698 A007318 * [1, 25, 25, 25, ...].
%F A139698 a(n) = 25*2^(n-1)-24. - _Emeric Deutsch_, May 03 2008
%F A139698 a(n) = 2*a(n-1) + 24 (with a(1)=1). - _Vincenzo Librandi_, Nov 24 2010
%F A139698 a(n) = 3*a(n-1)-2*a(n-2). G.f.: x*(23*x+1) / ((x-1)*(2*x-1)). - _Colin Barker_, Mar 11 2014
%e A139698 a(3) = 76 = (1, 2, 1) dot (1, 25, 25) = (1 + 50 + 25).
%p A139698 seq(25*2^(n-1)-24,n=1..25); # _Emeric Deutsch_, May 03 2008
%t A139698 LinearRecurrence[{3,-2},{1,26},40] (* _Harvey P. Dale_, Jul 25 2021 *)
%o A139698 (PARI) Vec(x*(23*x+1)/((x-1)*(2*x-1)) + O(x^100)) \\ _Colin Barker_, Mar 11 2014
%o A139698 (Magma) [25*2^(n-1)-24 : n in [1..40]]; // _Wesley Ivan Hurt_, Jan 17 2017
%Y A139698 Cf. A139634, A139635, A139697.
%K A139698 nonn,easy
%O A139698 1,2
%A A139698 _Gary W. Adamson_, Apr 29 2008
%E A139698 More terms from _Emeric Deutsch_, May 03 2008
%E A139698 More terms from _Colin Barker_, Mar 11 2014