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A143455 Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=4. 3
1, 4, 7, 10, 13, 16, 28, 49, 79, 118, 166, 250, 397, 634, 988, 1486, 2236, 3427, 5329, 8293, 12751, 19459, 29740, 45727, 70606, 108859, 167236, 256456, 393637, 605455, 932032, 1433740, 2203108, 3384019, 5200384, 7996480, 12297700, 18907024 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is also the number of length n quaternary words with at least 4 0-digits between any other digits.

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>=9, 4*a(n-9) equals the number of 4-colored compositions of n with all parts >=5, such that no adjacent parts have the same color. - Milan Janjic, Nov 27 2011

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: 1/(x^4*(1-x-3*x^5)).

MAPLE

a := proc(k::nonnegint) local n, i, j; if k=0 then unapply (4^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 3 else 0 fi)^(n+k))[1, 1], n) fi end(4): seq (a(n), n=0..50);

MATHEMATICA

Series[1/(1-x-3*x^5), {x, 0, 50}] // CoefficientList[#, x]& // Drop[#, 4]& (* Jean-Fran├žois Alcover, Feb 13 2014 *)

CROSSREFS

4th column of A143461.

Sequence in context: A182112 A090955 A134027 * A087065 A001197 A276874

Adjacent sequences:  A143452 A143453 A143454 * A143456 A143457 A143458

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Aug 16 2008

STATUS

approved

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Last modified September 26 15:27 EDT 2017. Contains 292531 sequences.