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%I #19 Nov 23 2018 22:13:15
%S 1,31,91,211,451,931,1891,3811,7651,15331,30691,61411,122851,245731,
%T 491491,983011,1966051,3932131,7864291,15728611,31457251,62914531,
%U 125829091,251658211,503316451,1006632931,2013265891,4026531811,8053063651,16106127331
%N Binomial transform of [1, 30, 30, 30, ...].
%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 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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A007318 * [1, 30, 30, 30, ...].
%F a(n) = 30*2^(n-1) - 29. - _Emeric Deutsch_, May 07 2008
%F a(n) = 2*a(n-1) + 29 (with a(1)=1). - _Vincenzo Librandi_, Nov 24 2010
%F From _Colin Barker_, Mar 11 2014: (Start)
%F a(n) = 3*a(n-1) - 2*a(n-2).
%F G.f.: x*(28*x+1) / ((x-1)*(2*x-1)). (End)
%e a(3) = 91 = (1, 2, 1) dot (1, 30, 30) = (1 + 60 + 30).
%p seq(30*2^(n-1)-29,n=1..27); # _Emeric Deutsch_, May 07 2008
%t LinearRecurrence[{3,-2},{1,31},30] (* _Harvey P. Dale_, Apr 18 2018 *)
%o (PARI) Vec(x*(28*x+1)/((x-1)*(2*x-1)) + O(x^100)) \\ _Colin Barker_, Mar 11 2014
%Y Cf. A139699, A139698, A139697, A139635, A139634.
%K nonn,easy
%O 1,2
%A _Gary W. Adamson_, Apr 29 2008
%E More terms from _Emeric Deutsch_, May 07 2008
%E More terms from _Colin Barker_, Mar 11 2014