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A015446
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Generalized Fibonacci numbers: a(n) = a(n-1) + 10*a(n-2).
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11
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1, 1, 11, 21, 131, 341, 1651, 5061, 21571, 72181, 287891, 1009701, 3888611, 13985621, 52871731, 192727941, 721445251, 2648724661, 9863177171, 36350423781, 134982195491, 498486433301, 1848308388211, 6833172721221
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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>=2, 11*a(n-2) equals the number of 11-colored compositions of n with all parts >=2, such that no adjacent parts have the same color.-Milan Janjic, Nov 26 2011
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
| a(n) = (((1+sqrt(41))/2)^(n+1) - ((1-sqrt(41))/2)^(n+1))/sqrt(41).
a(n) = sum{k=0..n, binomial((n+k)/2, k)*(1+(-1)^(n-k))*10^((n-k)/2)/2}; a(n)=sum{k=0..floor(n/2), binomial(n-k, k)10^k}; - Paul Barry, Sep 10 2005
a(n) is the entry (M^n)_1,1 where the matrix M = [1,2;5,0]. - Simone Severini, Jun 22 2006
a(n) = sum(k=0..n, A109466(n,k)*(-10)^(n-k) ). [From Philippe DELEHAM, Oct 26 2008]
G.f.: 1/(1-x-10*x^2). [Colin Barker, Feb 03 2012]
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MATHEMATICA
| Table[MatrixPower[{{1, 2}, {5, 0}}, n][[1]][[1]], {n, 0, 44}] [From Vladimir Orlovsky, Feb 20 2010]
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PROG
| (Sage) [lucas_number1(n, 1, -10) for n in xrange(1, 25)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
(MAGMA) [ n eq 1 select 1 else n eq 2 select 1 else Self(n-1)+10*Self(n-2): n in [1..30] ]; // Vincenzo Librandi, Aug 23 2011
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CROSSREFS
| Cf. A015447, A015443.
Sequence in context: A116525 A094623 A034922 * A083177 A110466 A110383
Adjacent sequences: A015443 A015444 A015445 * A015447 A015448 A015449
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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