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 A009978 #40 Jul 10 2025 10:59:44 %S A009978 1,34,1156,39304,1336336,45435424,1544804416,52523350144, %T A009978 1785793904896,60716992766464,2064377754059776,70188843638032384, %U A009978 2386420683693101056,81138303245565435904,2758702310349224820736,93795878551873643905024,3189059870763703892770816 %N A009978 Powers of 34. %C A009978 Same as Pisot sequences E(1, 34), L(1, 34), P(1, 34), T(1, 34). Essentially same as Pisot sequences E(34, 1156), L(34, 1156), P(34, 1156), T(34, 1156). See A008776 for definitions of Pisot sequences. %C A009978 The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n >= 1, a(n) equals the number of 34-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011 %H A009978 T. D. Noe, <a href="/A009978/b009978.txt">Table of n, a(n) for n=0..100</a> %H A009978 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>. %H A009978 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (34). %F A009978 G.f.: 1/(1-34*x). - _Philippe Deléham_, Nov 24 2008 %F A009978 a(n) = 34^n; a(n) = 34*a(n-1), n > 0; a(0)=1. - _Vincenzo Librandi_, Nov 21 2010 %F A009978 From _Elmo R. Oliveira_, Jul 10 2025: (Start) %F A009978 E.g.f.: exp(34*x). %F A009978 a(n) = A000079(n)*A001026(n). (End) %t A009978 34^Range[0,20] (* or *) NestList[34#&,1,20] (* _Harvey P. Dale_, May 03 2025 *) %o A009978 (Magma) [34^n: n in [0..100]]; // _Vincenzo Librandi_, Nov 21 2010 %Y A009978 Cf. A000079, A001026, A008776. %K A009978 nonn,easy %O A009978 0,2 %A A009978 _N. J. A. Sloane_