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A143460 Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=9. 2
1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 43, 64, 94, 133, 181, 238, 304, 379, 463, 556, 685, 877, 1159, 1558, 2101, 2815, 3727, 4864, 6253, 7921, 9976, 12607, 16084, 20758, 27061, 35506, 46687, 61279, 80038, 103801, 133729, 171550, 219802, 282076 (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 9 0-digits between any other digits.

LINKS

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

FORMULA

G.f.: 1/(x^9*(1-x-3*x^10)).

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(9): seq (a(n), n=0..61);

MATHEMATICA

Series[1/(1-x-3*x^10), {x, 0, 61}] // CoefficientList[#, x]& // Drop[#, 9]& (* Jean-Fran├žois Alcover, Feb 13 2014 *)

CROSSREFS

9th column of A143461.

Sequence in context: A112335 A016777 A308014 * A338701 A310679 A143459

Adjacent sequences:  A143457 A143458 A143459 * A143461 A143462 A143463

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Aug 16 2008

STATUS

approved

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Last modified October 21 21:51 EDT 2021. Contains 348155 sequences. (Running on oeis4.)