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 A165800 #48 Jul 09 2025 10:17:32 %S A165800 1,50,2500,125000,6250000,312500000,15625000000,781250000000, %T A165800 39062500000000,1953125000000000,97656250000000000, %U A165800 4882812500000000000,244140625000000000000,12207031250000000000000,610351562500000000000000,30517578125000000000000000,1525878906250000000000000000 %N A165800 Powers of 50. %C A165800 Same as Pisot sequences E(1, 50), L(1, 50), P(1, 50), T(1, 50). Essentially same as Pisot sequences E(50, 2500), L(50, 2500), P(50, 2500), T(50, 2500). See A008776 for definitions of Pisot sequences. %C A165800 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 50-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011 %H A165800 T. D. Noe, <a href="/A165800/b165800.txt">Table of n, a(n) for n = 0..100</a> %H A165800 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (50). %F A165800 G.f.: 1/(1-50*x). %F A165800 a(n) = 50^n; a(n) = 50*a(n-1) a(0)=1. - _Vincenzo Librandi_, Nov 21 2010 %F A165800 From _G. C. Greubel_, Apr 08 2016: (Start) %F A165800 a(n) = 2^n * 5^(2*n) = A000079(n)*A000351(n)^2. %F A165800 a(n) = 5^n * 10^n = A000351(n)*A011557(n). (End) %F A165800 From _Elmo R. Oliveira_, Jul 08 2025: (Start) %F A165800 E.g.f.: exp(50*x). %F A165800 a(n) = A098608(n)/A000079(n). (End) %t A165800 50^Range[0, 20] (* _Paolo Xausa_, Jul 09 2025 *) %o A165800 (Magma) [50^n: n in [0..20]]; // _Vincenzo Librandi_, Nov 21 2010 %o A165800 (Maxima) A165800(n):=50^n$ %o A165800 makelist(A165800(n),n,0,30); /* _Martin Ettl_, Nov 06 2012 */ %o A165800 (PARI) a(n)=50^n \\ _Charles R Greathouse IV_, Jun 19 2015 %o A165800 (PARI) powers(50,8) \\ _Charles R Greathouse IV_, Jun 19 2015 %Y A165800 Cf. A000079, A000351, A008776, A011557, A098608. %K A165800 nonn,easy %O A165800 0,2 %A A165800 _Jaroslav Krizek_, Sep 27 2009