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A047856 a(n) = A047848(8, n).

%I A047856 #32 Jan 14 2025 10:30:57
%S A047856 1,2,13,134,1465,16106,177157,1948718,21435889,235794770,2593742461,
%T A047856 28531167062,313842837673,3452271214394,37974983358325,
%U A047856 417724816941566,4594972986357217,50544702849929378,555991731349223149,6115909044841454630,67274999493256000921,740024994425816010122
%N A047856 a(n) = A047848(8, n).
%C A047856 n-th difference of a(n), a(n-1), ..., a(0) is A011557(n-1) for n >= 1.
%H A047856 G. C. Greubel, <a href="/A047856/b047856.txt">Table of n, a(n) for n = 0..955</a>
%H A047856 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-11).
%F A047856 a(n) = (11^n + 9)/10. - _Ralf Stephan_, Feb 14 2004
%F A047856 From _Philippe Deléham_, Oct 06 2009: (Start)
%F A047856 a(0) = 1, a(1) = 2, a(n) = 12*a(n-1) - 11*a(n-2) for n > 1.
%F A047856 G.f.: (1 - 10*x)/(1 - 12*x + 11*x^2). (End)
%F A047856 a(n) = 11*a(n-1) - 9, with a(0)=1. - _Vincenzo Librandi_, Aug 06 2010
%F A047856 E.g.f.: exp(x)*(exp(10*x) + 9)/10. - _Elmo R. Oliveira_, Aug 30 2024
%p A047856 a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=11*a[n-1]+1 od: seq(a[n]+1, n=0..16); # _Zerinvary Lajos_, Mar 20 2008
%t A047856 (11^Range[0,40] +9)/10 (* _G. C. Greubel_, Jan 12 2025 *)
%o A047856 (Magma) [(11^n +9)/10: n in [0..40]]; // _G. C. Greubel_, Jan 12 2025
%o A047856 (Python)
%o A047856 def A047856(n): return (pow(11, n) + 9)//10
%o A047856 print([A047856(n) for n in range(41)]) # _G. C. Greubel_, Jan 12 2025
%Y A047856 Cf. A011557, A047848.
%K A047856 nonn,easy
%O A047856 0,2
%A A047856 _Clark Kimberling_
%E A047856 a(17)-a(21) from _Elmo R. Oliveira_, Aug 30 2024