This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A047850 #34 Jan 10 2025 18:52:47 %S A047850 1,2,7,32,157,782,3907,19532,97657,488282,2441407,12207032,61035157, %T A047850 305175782,1525878907,7629394532,38146972657,190734863282, %U A047850 953674316407,4768371582032,23841857910157,119209289550782,596046447753907 %N A047850 a(n) = (5^n + 3)/4. %H A047850 G. C. Greubel, <a href="/A047850/b047850.txt">Table of n, a(n) for n = 0..1000</a> %H A047850 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-5). %F A047850 a(n) = A047848(2,n). %F A047850 From _Philippe Deléham_, Oct 06 2009: (Start) %F A047850 a(n) = 6*a(n-1) - 5*a(n-2) for n > 1. %F A047850 G.f.: (1-4*x)/((1-x)*(1-5*x)). (End) %F A047850 a(n) = 5*a(n-1) - 3 (with a(0)=1). - _Vincenzo Librandi_, Aug 06 2010 %F A047850 From _Elmo R. Oliveira_, Dec 10 2023: (Start) %F A047850 a(n) = A132079(n)/2. %F A047850 E.g.f.: (1/4)*(exp(5*x) + 3*exp(x)). (End) %t A047850 (5^Range[0,40] +3)/4 (* _G. C. Greubel_, Jan 10 2025 *) %o A047850 (PARI) a(n)=(5^n+3)/4 \\ _Charles R Greathouse IV_, Oct 07 2015 %o A047850 (Magma) A047850:= func< n | (5^n + 3)/4 >; [A047850(n): n in [0..40]]; // _G. C. Greubel_, Jan 10 2025 %o A047850 (Python) %o A047850 def A047850(n): return (5^n+3)//4 %o A047850 print([A047850(n) for n in range(41)]) # _G. C. Greubel_, Jan 10 2025 %Y A047850 Cf. A047848, A132079. %K A047850 nonn,easy %O A047850 0,2 %A A047850 _Clark Kimberling_ %E A047850 Better description from _Michael Somos_