cp's OEIS Frontend

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.

A178681 a(n) = 6^n + 6.

This page as a plain text file.
%I A178681 #39 Sep 08 2022 08:45:54
%S A178681 7,12,42,222,1302,7782,46662,279942,1679622,10077702,60466182,
%T A178681 362797062,2176782342,13060694022,78364164102,470184984582,
%U A178681 2821109907462,16926659444742,101559956668422,609359740010502
%N A178681 a(n) = 6^n + 6.
%H A178681 Vincenzo Librandi, <a href="/A178681/b178681.txt">Table of n, a(n) for n = 0..1000</a>
%H A178681 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-6).
%F A178681 a(n) = 6*(a(n-1)-5), n > 0.
%F A178681 a(n) = 7*a(n-1) - 6*a(n-2).
%F A178681 a(n) = 6*A062394(n-1), n > 0.
%F A178681 G.f.: (7-37*x)/((1-x)*(1-6*x)). - _Klaus Brockhaus_, Dec 27 2010
%F A178681 a(n) = A000400(n) + 6. - _Michel Marcus_, Nov 23 2013
%F A178681 E.g.f.: exp(6*x) + 6*exp(x). - _G. C. Greubel_, Jan 26 2019
%t A178681 LinearRecurrence[{7,-6},{7,12},41] (* or *) 6^Range[0,40]+6 (* _Harvey P. Dale_, Aug 11 2011 *)
%o A178681 (Magma) [ 6^n+6: n in [0..25] ];
%o A178681 (PARI) for(n=0,25,print1(6^n+6,",")) \\ _Edward Jiang_, Nov 22 2013
%o A178681 (Sage) [6^n +6 for n in range(25)] # _G. C. Greubel_, Jan 26 2019
%o A178681 (GAP) List([0..25], n -> 6^n + 6); # _G. C. Greubel_, Jan 26 2019
%Y A178681 Cf. A000400, A052934 (first differences).
%K A178681 nonn,easy
%O A178681 0,1
%A A178681 _Vincenzo Librandi_, Dec 25 2010