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A143456
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Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=5.
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2
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1, 4, 7, 10, 13, 16, 19, 31, 52, 82, 121, 169, 226, 319, 475, 721, 1084, 1591, 2269, 3226, 4651, 6814, 10066, 14839, 21646, 31324, 45277, 65719, 95917, 140434, 205372, 299344, 435175, 632332, 920083, 1341385, 1957501, 2855533, 4161058, 6058054
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OFFSET
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0,2
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COMMENTS
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a(n) is also the number of length n quaternary words with at least 5 0-digits between any other digits.
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LINKS
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Table of n, a(n) for n=0..39.
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FORMULA
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G.f.: 1/(x^5*(1-x-3*x^6)).
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MAPLE
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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(5): seq (a(n), n=0..52);
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CROSSREFS
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5th column of A143461.
Sequence in context: A143457 A046956 A198265 * A090852 A182112 A090955
Adjacent sequences: A143453 A143454 A143455 * A143457 A143458 A143459
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Aug 16 2008
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STATUS
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approved
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