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A120691
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First differences of coefficients in the continued fraction for e.
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3
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2, -1, 1, -1, 0, 3, -3, 0, 5, -5, 0, 7, -7, 0, 9, -9, 0, 11, -11, 0, 13, -13, 0, 15, -15, 0, 17, -17, 0, 19, -19, 0, 21, -21, 0, 23, -23, 0, 25, -25, 0, 27, -27, 0, 29, -29, 0, 31, -31, 0, 33, -33, 0, 35, -35, 0, 37, -37, 0, 39, -39
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OFFSET
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0,1
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COMMENTS
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First differences of A003417.
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LINKS
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Table of n, a(n) for n=0..60.
Index entries for linear recurrences with constant coefficients, signature (-1,-1,1,1,1).
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FORMULA
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G.f.: (1-x)(2+x+2x^2-3x^3-x^4+x^6)/(1-2x^3+x^6);
a(n)=2*C(0,n)-C(1,n)+2*sin(2*pi*(n-1)/3)*floor((2n-1)/3)/sqrt(3). [Sign corrected by M. F. Hasler, May 01 2013]
a(0)=2, a(1)=-1, for n>0: a(3n-1)=2n-1, a(3n)=1-2n, a(3n+1)=0. - M. F. Hasler, May 01 2013
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MATHEMATICA
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Join[{2}, Differences[ContinuedFraction[E, 120]]] (* or *) LinearRecurrence[ {-1, -1, 1, 1, 1}, {2, -1, 1, -1, 0, 3, -3}, 120] (* Harvey P. Dale, Jun 08 2016 *)
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PROG
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(PARI) A120691(n)={n<2 && return(2-3*n); n=divrem(n-1, 3); if(n[2], -(1+n[1]*2)*(-1)^n[2])} \\ - M. F. Hasler, May 01 2013
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CROSSREFS
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Cf. A102899.
Sequence in context: A249303 A182662 A127284 * A111941 A153462 A126310
Adjacent sequences: A120688 A120689 A120690 * A120692 A120693 A120694
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry, Jun 27 2006
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STATUS
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approved
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