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A255386
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Number of binary words of length n with exactly one occurrence of subword 010 and exactly one occurrence of subword 101.
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6
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0, 0, 0, 0, 2, 4, 10, 20, 42, 84, 166, 320, 608, 1140, 2116, 3892, 7102, 12868, 23170, 41488, 73918, 131104, 231578, 407520, 714672, 1249368, 2177736, 3785688, 6564362, 11355940, 19602154, 33767228, 58056786, 99638364, 170711134, 292011872, 498747632
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OFFSET
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0,5
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LINKS
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FORMULA
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G.f.: -2*x^4*(x-1)^2/((x^2-x+1)*(x^2+x-1)^3).
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EXAMPLE
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a(4) = 2: 0101, 1010.
a(5) = 4: 00101, 01011, 10100, 11010.
a(6) = 10: 000101, 001011, 010110, 010111, 011010, 100101, 101000, 101001, 110100, 111010.
a(8) = 42: 00000101, 00001011, 00010110, 00010111, 00011010, 00101100, 00101110, 00101111, 00110100, 00111010, 01001101, 01011000, 01011001, 01011100, 01011110, 01011111, 01100101, 01101000, 01101001, 01110100, 01111010, 10000101, 10001011, 10010110, 10010111, 10011010, 10100000, 10100001, 10100011, 10100110, 10100111, 10110010, 11000101, 11001011, 11010000, 11010001, 11010011, 11100101, 11101000, 11101001, 11110100, 11111010.
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MAPLE
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a:= n-> coeff(series(-2*x^4*(x-1)^2/
((x^2-x+1)*(x^2+x-1)^3), x, n+1), x, n):
seq(a(n), n=0..50);
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MATHEMATICA
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LinearRecurrence[{4, -4, -2, 5, -2, -2, 2, 1}, {0, 0, 0, 0, 2, 4, 10, 20}, 40] (* Harvey P. Dale, Apr 09 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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