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A167762
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a(n) = 2*a(n-1)+3*a(n-2)-6*a(n-3) starting a(0)=a(1)=0, a(2)=1.
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4
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0, 0, 1, 2, 7, 14, 37, 74, 175, 350, 781, 1562, 3367, 6734, 14197, 28394, 58975, 117950, 242461, 484922, 989527, 1979054, 4017157, 8034314, 16245775, 32491550, 65514541, 131029082, 263652487, 527304974, 1059392917, 2118785834, 4251920575, 8503841150
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OFFSET
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0,4
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COMMENTS
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Inverse binomial transform yields two zeros followed by A077917 (a signed variant of A127864).
a(n) mod 10 is zero followed by a sequence with period length 8: 0, 1, 2, 7, 4, 7, 4, 5 (repeat).
a(n) is the number of length n+1 binary words with some prefix w such that w contains three more 1's than 0's and no prefix of w contains three more 0's than 1's. - Geoffrey Critzer, Dec 13 2013
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2, 3, -6).
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FORMULA
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a(n) mod 9 = A153130(n), n>3 (essentially the same as A154529, A146501 and A029898).
a(n+1)-2*a(n) = 0 if n even, = A000244((1+n)/2) if n odd.
a(2*n) = A005061(n). a(2*n+1) = 2*A005061(n).
G.f.: x^2/((2*x-1)*(3*x^2-1)). a(n) = 2^n - A038754(n). - R. J. Mathar, Nov 12 2009
G.f.: x^2/(1-2*x-3*x^2+6*x^3). - Philippe Deléham, Nov 11 2009
a(n) = -3*(-sqrt(3))^n*(-18-12*sqrt(3))^(-1) -12*2^n*sqrt(3)*(-18-12*sqrt(3))^(-1) +12 *sqrt(3)*3^(1/2*n)*(-18-12*sqrt(3))^(-1) -18*2^n*(-18-12*sqrt(3))^(-1) +21*3^(1/2 *n)*(-18-12*sqrt(3))^(-1), with n>=0. - Paolo P. Lava, Nov 16 2009
a(n) = [ -18-12*sqrt(3)]^(-1)*{12*sqrt(3)*[3^((1/2)*n)-2^n]+21*3^((1/2)*n)-3*(-sqrt(3))^n-18*2^n}, with n>=0. - Paolo P. Lava, Nov 16 2009
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MATHEMATICA
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LinearRecurrence[{2, 3, -6}, {0, 0, 1}, 40] (* Harvey P. Dale, Sep 17 2013 *)
CoefficientList[Series[x^2/((2 x - 1) (3 x^2 - 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Sep 17 2013 *)
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CROSSREFS
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Cf. A024495, A167710.
Sequence in context: A173126 A256272 A320651 * A191389 A191319 A018497
Adjacent sequences: A167759 A167760 A167761 * A167763 A167764 A167765
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KEYWORD
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nonn,easy
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AUTHOR
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Paul Curtz, Nov 11 2009
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EXTENSIONS
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Edited and extended by R. J. Mathar, Nov 12 2009
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STATUS
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approved
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