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A143448 Expansion of 1/(x^k*(1-x-2*x^(k+1))) for k=5. 3
1, 3, 5, 7, 9, 11, 13, 19, 29, 43, 61, 83, 109, 147, 205, 291, 413, 579, 797, 1091, 1501, 2083, 2909, 4067, 5661, 7843, 10845, 15011, 20829, 28963, 40285, 55971, 77661, 107683, 149341, 207267, 287837, 399779, 555101, 770467, 1069149, 1483683, 2059357, 2858915 (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>=11, 3*a(n-11) equals the number of 3-colored compositions of n with all parts >=6, such that no adjacent parts have the same color. - Milan Janjic, Nov 27 2011

a(n) equals the number of ternary words of length n having at least 5 zeros between every two successive nonzero letters. - Milan Janjic, Mar 09 2015

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,2).

FORMULA

G.f.: 1/(x^5*(1-x-2*x^6)).

a(n) = 2n+1 if n<=6, else a(n) = a(n-1) + 2a(n-6). - Milan Janjic, Mar 09 2015

MAPLE

a:= proc(k::nonnegint) local n, i, j; if k=0 then unapply(3^n, n) else unapply((Matrix(k+1, (i, j)-> if (i=j-1) or j=1 and i=1 then 1 elif j=1 and i=k+1 then 2 else 0 fi)^(n+k))[1, 1], n) fi end(5): seq(a(n), n=0..56);

MATHEMATICA

Series[1/(1-x-2*x^6), {x, 0, 56}] // CoefficientList[#, x]& // Drop[#, 5]& (* Jean-Fran├žois Alcover, Feb 13 2014 *)

CROSSREFS

5th column of A143453.

Sequence in context: A133854 A239008 A030155 * A226484 A261213 A130738

Adjacent sequences:  A143445 A143446 A143447 * A143449 A143450 A143451

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 16 2008

STATUS

approved

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Last modified August 19 23:35 EDT 2017. Contains 290821 sequences.