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A003410
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Expansion of (1+x)(1+x^2)/(1-x-x^3).
(Formerly M0648)
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15
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1, 2, 3, 5, 7, 10, 15, 22, 32, 47, 69, 101, 148, 217, 318, 466, 683, 1001, 1467, 2150, 3151, 4618, 6768, 9919, 14537, 21305, 31224, 45761, 67066, 98290, 144051, 211117, 309407, 453458, 664575, 973982, 1427440, 2092015, 3065997, 4493437, 6585452, 9651449
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OFFSET
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0,2
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COMMENTS
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a(n) is the number of binary words of length n that have no pair of adjacent 1's and have no 0000 subwords. Example: a(4)=7 because we have 0101, 1010, 0010, 1001, 0100, 0001, and 1000.
a(n) is the number of solus bitstrings of length n with no runs of 4 zeros. - Steven Finch, Mar 25 2020
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REFERENCES
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R. K. Guy, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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MAPLE
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G:=series((1+x)*(1+x^2)/(1-x-x^3), x=0, 42): 1, seq(coeff(G, x^n), n=1..38);
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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