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Search: id:A143454
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| A143454 |
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Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=3. |
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+0
2
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| 1, 4, 7, 10, 13, 25, 46, 76, 115, 190, 328, 556, 901, 1471, 2455, 4123, 6826, 11239, 18604, 30973, 51451, 85168, 140980, 233899, 388252, 643756, 1066696, 1768393, 2933149, 4864417, 8064505, 13369684, 22169131, 36762382, 60955897, 101064949
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) is also the number of length n quaternary words with at least 3 0-digits between any other digits.
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FORMULA
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G.f.: 1/(x^3*(1-x-3*x^4)).
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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(3): seq (a(n), n=0..47);
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CROSSREFS
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3rd column of A143461.
Sequence in context: A069212 A091290 A119256 this_sequence A065810 A123837 A125620
Adjacent sequences: A143451 A143452 A143453 this_sequence A143455 A143456 A143457
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 16 2008
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