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A015447
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Generalized Fibonacci numbers: a(n) = a(n-1) + 11*a(n-2).
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16
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1, 1, 12, 23, 155, 408, 2113, 6601, 29844, 102455, 430739, 1557744, 6295873, 23431057, 92685660, 350427287, 1369969547, 5224669704, 20294334721, 77765701465, 301003383396, 1156426099511, 4467463316867, 17188150411488
(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, 12*a(n-2) equals the number of 12-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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FORMULA
| a(n)={[ (1+3*sqrt(5))/2 ]^(n+1) - [ (1-3*sqrt(5))/2 ]^(n+1)}/3*sqrt(5).
a(n-1)=(1/3)*(-1)^n*sum(i=0, n, (-3)^i*F(i)*C(n, i)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 06 2004
a(n)=Sum_{k, 0<=k<=n} A109466(n,k)*(-11)^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 26 2008]
G.f.: 1/(1-x-11*x^2) [From Harvey P. Dale, May 08 2011]
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MATHEMATICA
| Join[{a=1, b=1}, Table[c=b+11*a; a=b; b=c, {n, 100}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 16 2011*)
LinearRecurrence[{1, 11}, {1, 1}, 30] (* or *) CoefficientList[Series[ 1/(1-x-11 x^2), {x, 0, 50}], x] (* From Harvey P. Dale, May 08 2011 *)
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PROG
| (Sage) [lucas_number1(n, 1, -11) for n in xrange(0, 27)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
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CROSSREFS
| Cf. A015446, A015443.
Sequence in context: A045532 A190426 A083683 * A072822 A059161 A133491
Adjacent sequences: A015444 A015445 A015446 * A015448 A015449 A015450
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KEYWORD
| nonn,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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