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A047853 a(n) = A047848(5, n).

%I A047853 #43 Jan 14 2025 10:30:32
%S A047853 1,2,10,74,586,4682,37450,299594,2396746,19173962,153391690,
%T A047853 1227133514,9817068106,78536544842,628292358730,5026338869834,
%U A047853 40210710958666,321685687669322,2573485501354570,20587884010836554,164703072086692426,1317624576693539402,10540996613548315210
%N A047853 a(n) = A047848(5, n).
%C A047853 n-th difference of a(n), a(n-1), ..., a(0) is A000420(n-1) for n >= 1.
%H A047853 Vincenzo Librandi, <a href="/A047853/b047853.txt">Table of n, a(n) for n = 0..200</a>
%H A047853 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-8).
%F A047853 a(n) = (8^n + 6)/7. - _Ralf Stephan_, Feb 14 2004
%F A047853 From _Philippe Deléham_, Oct 05 2009: (Start)
%F A047853 a(0)=1, a(1)=2; a(n) = 9*a(n-1) - 8*a(n-2) for n>1.
%F A047853 G.f.: (1 - 7*x)/(1 - 9*x + 8*x^2). (End)
%F A047853 a(n) = 8*a(n-1) - 6 for n>0, a(0)=1. - _Vincenzo Librandi_, Aug 06 2010
%F A047853 a(n+1) = A226308(3*n). - _Philippe Deléham_, Feb 24 2014
%F A047853 E.g.f.: exp(x)*(6 + exp(7*x))/7. - _Stefano Spezia_, Oct 16 2023
%p A047853 a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=8*a[n-1]+1 od: seq(a[n]+1, n=0..18); # _Zerinvary Lajos_, Mar 20 2008
%t A047853 LinearRecurrence[{9, -8}, {1, 2}, 30] (* _Harvey P. Dale_, Dec 11 2016 *)
%t A047853 (8^Range[0,40] +6)/7 (* _G. C. Greubel_, Jan 12 2025 *)
%o A047853 (Magma) [(8^n +6)/7: n in [0..40]]; // _G. C. Greubel_, Jan 12 2025
%o A047853 (Python)
%o A047853 def A047853(n): return (pow(8,n) +6)//7
%o A047853 print([A047853(n) for n in range(41)]) # _G. C. Greubel_, Jan 12 2025
%Y A047853 Cf. A000420, A047848, A226308.
%K A047853 nonn,easy
%O A047853 0,2
%A A047853 _Clark Kimberling_
%E A047853 More terms from _Vladimir Joseph Stephan Orlovsky_, Nov 07 2008