cp's OEIS Frontend

A047854 a(n) = A047848(6, n).

%I A047854 #38 Jan 14 2025 10:30:40
%S A047854 1,2,11,92,821,7382,66431,597872,5380841,48427562,435848051,
%T A047854 3922632452,35303692061,317733228542,2859599056871,25736391511832,
%U A047854 231627523606481,2084647712458322,18761829412124891,168856464709124012,1519708182382116101,13677373641439044902,123096362772951404111
%N A047854 a(n) = A047848(6, n).
%C A047854 n-th difference of a(n), a(n-1), ..., a(0) is A001018(n-1) for n >= 1.
%C A047854 Also, the cogrowth sequence of the 16-element group D4 X C2 = <S,T,U | S^4, T^2, U^2, (ST)^2, [S,T], [U,T]>. - _Sean A. Irvine_, Nov 10 2024
%H A047854 G. C. Greubel, <a href="/A047854/b047854.txt">Table of n, a(n) for n = 0..1000</a>
%H A047854 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-9).
%F A047854 a(n) = (9^n + 7)/8. - _Ralf Stephan_, Feb 14 2004
%F A047854 From _Philippe Deléham_, Oct 06 2009: (Start)
%F A047854 a(0) = 1, a(1) = 2, a(n) = 10*a(n-1) - 9*a(n-2) for n > 1.
%F A047854 G.f.: (1 - 8*x)/(1 - 10*x + 9*x^2). (End)
%F A047854 a(n) = 9*a(n-1) - 7 (with a(0)=1). - _Vincenzo Librandi_, Aug 06 2010
%F A047854 E.g.f.: exp(x)*(exp(8*x) + 7)/8. - _Elmo R. Oliveira_, Aug 29 2024
%p A047854 a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=9*a[n-1]+1 od: seq(a[n]+1, n=0..17); # _Zerinvary Lajos_, Mar 20 2008
%t A047854 a = {1}; ZZ = 1; Do[ZZ = ZZ + 3^(2x); AppendTo[a, ZZ], {x,0,40}]; a (* _Zerinvary Lajos_, Apr 03 2007 *)
%t A047854 (9^Range[0,40] +7)/8 (* _G. C. Greubel_, Jan 12 2025 *)
%o A047854 (Magma) [(9^n +7)/8: n in [0..40]]; // _G. C. Greubel_, Jan 12 2025
%o A047854 (Python)
%o A047854 def A047854(n): return (pow(9,n) +7)//8
%o A047854 print([A047854(n) for n in range(41)]) # _G. C. Greubel_, Jan 12 2025
%Y A047854 Cf. A001018, A047848.
%K A047854 nonn,easy
%O A047854 0,2
%A A047854 _Clark Kimberling_
%E A047854 a(18)-a(22) from _Elmo R. Oliveira_, Aug 29 2024