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A006085
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Continued fraction for e/4.
(Formerly M1822)
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5
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0, 1, 2, 8, 3, 1, 1, 1, 1, 7, 1, 1, 2, 1, 1, 1, 2, 7, 1, 2, 2, 1, 1, 1, 3, 7, 1, 3, 2, 1, 1, 1, 4, 7, 1, 4, 2, 1, 1, 1, 5, 7, 1, 5, 2, 1, 1, 1, 6, 7, 1, 6, 2, 1, 1, 1, 7, 7, 1, 7, 2, 1, 1, 1, 8, 7, 1, 8, 2, 1, 1, 1, 9, 7, 1, 9, 2, 1, 1, 1, 10, 7, 1, 10, 2, 1, 1, 1, 11, 7, 1, 11, 2, 1, 1, 1, 12, 7, 1, 12, 2, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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REFERENCES
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D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 2, p. 601.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1).
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FORMULA
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First seven terms are 0, 1, 2, 8, 3, 1, 1; then a(8k)=1, a(8k+1)=k, a(8k+2)=7, a(8k+3)=1, a(8k+4)=k, a(8k+5)=2, a(8k+6)=1, a(8k+7)=1. - Benoit Cloitre, Apr 08 2003
G.f.: x*(1+x+7*x^2-4*x^3+5*x^4-4*x^5+5*x^6-4*x^7+9*x^8-12*x^9-3*x^10-x^11-x^13-6*x^16+7*x^17+x^18) / ((1-x)^2*(1+x)*(1+x^2)^2*(1+x^4)^2). - Colin Barker, May 16 2016
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EXAMPLE
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0.679570457114761308840071867... = 0 + 1/(1 + 1/(2 + 1/(8 + 1/(3 + ...)))). - Harry J. Smith, May 10 2009
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MATHEMATICA
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Join[{0, 1, 2, 8, 3}, LinearRecurrence[{1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1}, {1, 1, 1, 1, 7, 1, 1, 2, 1, 1, 1, 2, 7, 1, 2}, 97]] (* Ray Chandler, Sep 03 2015 *)
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PROG
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(PARI) { allocatemem(932245000); default(realprecision, 40000); x=contfrac(exp(1)/4); for (n=1, 20000, write("b006085.txt", n, " ", x[n])); } \\ Harry J. Smith, May 10 2009
(PARI) concat(0, Vec(x*(1+x+7*x^2-4*x^3+5*x^4-4*x^5+5*x^6-4*x^7+9*x^8-12*x^9-3*x^10-x^11-x^13-6*x^16+7*x^17+x^18)/((1-x)^2*(1+x)*(1+x^2)^2*(1+x^4)^2) + O(x^50))) \\ Colin Barker, May 16 2016
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CROSSREFS
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KEYWORD
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nonn,cofr,easy
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AUTHOR
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EXTENSIONS
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More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 20 2003
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STATUS
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approved
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