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A306315
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Number of binary words of length n such that the difference between the number of 1's and the number of 0's is in the interval [-2,3] for every prefix and in the interval [-3,2] for every suffix.
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3
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1, 2, 4, 6, 12, 18, 35, 54, 103, 162, 307, 486, 926, 1458, 2823, 4374, 8688, 13122, 26962, 39366, 84285, 118098, 265147, 354294, 838625, 1062882, 2664636, 3188646, 8499263, 9565938, 27197074, 28697814, 87261592, 86093442, 280596321, 258280326, 903916589
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OFFSET
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0,2
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..3911
Index entries for linear recurrences with constant coefficients, signature (0,11,0,-46,0,90,0,-81,0,28,0,-3)
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FORMULA
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G.f.: -(2*x^11-18*x^9+9*x^8+48*x^7+3*x^6-44*x^5-14*x^4+16*x^3+7*x^2-2*x-1) / ((3*x^2-1) *(x^2+x-1) *(x^2-x-1) *(x^3-2*x^2-x+1) *(x^3+2*x^2-x-1)).
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EXAMPLE
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a(3) = 6: 001, 010, 011, 100, 101, 110.
a(4) = 12: 0010, 0011, 0100, 0101, 0110, 1000, 1001, 1010, 1011, 1100, 1101, 1110.
a(5) = 18: 00101, 00110, 01001, 01010, 01011, 01100, 01101, 01110, 10001, 10010, 10011, 10100, 10101, 10110, 11000, 11001, 11010, 11100.
a(6) = 35: 001010, 001011, 001100, 001101, 001110, 010010, 010011, 010100, 010101, 010110, 011000, 011001, 011010, 011100, 100010, 100011, 100100, 100101, 100110, 101000, 101001, 101010, 101011, 101100, 101101, 101110, 110001, 110010, 110011, 110100, 110101, 110110, 111000, 111001, 111010.
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MATHEMATICA
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LinearRecurrence[{0, 11, 0, -46, 0, 90, 0, -81, 0, 28, 0, -3}, {1, 2, 4, 6, 12, 18, 35, 54, 103, 162, 307, 486}, 40] (* Harvey P. Dale, Sep 17 2019 *)
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CROSSREFS
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Odd bisection gives A008776.
Cf. A306293, A306306.
Sequence in context: A331933 A052823 A063516 * A104352 A133488 A351016
Adjacent sequences: A306312 A306313 A306314 * A306316 A306317 A306318
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KEYWORD
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nonn,easy
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AUTHOR
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Alois P. Heinz, Feb 06 2019
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STATUS
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approved
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