cp's OEIS Frontend

A047852 a(n) = A047848(4, n).

%I A047852 #30 Jan 12 2025 05:27:44
%S A047852 1,2,9,58,401,2802,19609,137258,960801,6725602,47079209,329554458,
%T A047852 2306881201,16148168402,113037178809,791260251658,5538821761601,
%U A047852 38771752331202,271402266318409,1899815864228858,13298711049602001,93090977347214002,651636841430498009,4561457890013486058
%N A047852 a(n) = A047848(4, n).
%C A047852 n-th difference of a(n), a(n-1), ..., a(0) is A000400(n-1) for n >= 1.
%H A047852 G. C. Greubel, <a href="/A047852/b047852.txt">Table of n, a(n) for n = 0..1000</a>
%H A047852 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-7).
%F A047852 a(n) = (7^n + 5)/6. - _Ralf Stephan_, Feb 14 2004
%F A047852 From _Philippe Deléham_, Oct 06 2009: (Start)
%F A047852 a(0) = 1, a(1) = 2, a(n) = 8*a(n-1) - 7*a(n-2) for n > 1.
%F A047852 G.f.: (1 - 6*x)/(1 - 8*x + 7*x^2). (End)
%F A047852 a(n) = 7*a(n-1) - 5, with a(0)=1. - _Vincenzo Librandi_, Aug 06 2010
%F A047852 E.g.f.: exp(x)*(exp(6*x) + 5)/6. - _Elmo R. Oliveira_, Aug 29 2024
%p A047852 a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=7*a[n-1]+1 od: seq(a[n]+1, n=0..19); # _Zerinvary Lajos_, Mar 20 2008
%t A047852 (7^Range[0,40] +5)/6 (* _G. C. Greubel_, Jan 12 2025 *)
%o A047852 (Magma) [(7^n +5)/6: n in [0..40]]; // _G. C. Greubel_, Jan 12 2025
%o A047852 (Python)
%o A047852 def A047852(n): return (pow(7, n) + 5)//6
%o A047852 print([A047852(n) for n in range(41)]) # _G. C. Greubel_, Jan 12 2025
%Y A047852 Cf. A000400, A047848.
%K A047852 nonn,easy
%O A047852 0,2
%A A047852 _Clark Kimberling_
%E A047852 a(20)-a(23) from _Elmo R. Oliveira_, Aug 29 2024