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 A009965 Powers of 21. 29
 1, 21, 441, 9261, 194481, 4084101, 85766121, 1801088541, 37822859361, 794280046581, 16679880978201, 350277500542221, 7355827511386641, 154472377739119461, 3243919932521508681, 68122318582951682301, 1430568690241985328321, 30041942495081691894741, 630880792396715529789561, 13248496640331026125580781, 278218429446951548637196401 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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 21-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011 LINKS T. D. Noe, Table of n, a(n) for n = 0..100 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (21). FORMULA For A009966..A009992 we have g.f.: 1/(1-qx), e.g.f.: exp(qx), with q = 21, 22, ..., 48. - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 07 2001 a(n) = 21^n; a(n) = 21*a(n-1), n > 0, a(0)=1. - Vincenzo Librandi, Nov 21 2010 G.f.: 22/G(0) where G(k) = 1 - 2*x*(k+1)/(1 - 1/(1 - 2*x*(k+1)/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 10 2013 PROG (Sage) [lucas_number1(n, 21, 0) for n in range(1, 17)] # Zerinvary Lajos, Apr 29 2009 (MAGMA) [21^n: n in [0..100]] // Vincenzo Librandi, Nov 21 2010 (PARI) a(n)=21^n \\ Charles R Greathouse IV, Nov 18 2011 (Maxima) A009965(n):=21^n\$ makelist(A009965(n), n, 0, 30); /* Martin Ettl, Nov 07 2012 */ CROSSREFS Row 10 of A329332. Sequence in context: A224009 A167255 A171295 * A285873 A189433 A041842 Adjacent sequences:  A009962 A009963 A009964 * A009966 A009967 A009968 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified May 30 05:35 EDT 2020. Contains 334712 sequences. (Running on oeis4.)