

A120691


First differences of coefficients in the continued fraction for e.


3



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

0,1


COMMENTS

First differences of A003417.


LINKS

Table of n, a(n) for n=0..60.
Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1).


FORMULA

G.f.: (1x)(2+x+2x^23x^3x^4+x^6)/(12x^3+x^6);
a(n)=2*C(0,n)C(1,n)+2*sin(2*pi*(n1)/3)*floor((2n1)/3)/sqrt(3). [Sign corrected by M. F. Hasler, May 01 2013]
a(0)=2, a(1)=1, for n>0: a(3n1)=2n1, a(3n)=12n, a(3n+1)=0.  M. F. Hasler, May 01 2013


PROG

(PARI) A120691(n)={n<2 && return(23*n); n=divrem(n1, 3); if(n[2], (1+n[1]*2)*(1)^n[2])} \\  M. F. Hasler, May 01 2013


CROSSREFS

Cf. A102899.
Sequence in context: A249303 A182662 A127284 * A111941 A153462 A126310
Adjacent sequences: A120688 A120689 A120690 * A120692 A120693 A120694


KEYWORD

easy,sign


AUTHOR

Paul Barry, Jun 27 2006


STATUS

approved



