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Search: id:A072347
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| A072347 |
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If n = pqr...st in binary, a(n) = value of continuant [p,q,r,...,s,t]. |
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+0
3
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| 1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 2, 3, 2, 5, 1, 2, 1, 3, 2, 3, 2, 5, 1, 3, 1, 4, 3, 5, 3, 8, 1, 2, 1, 3, 2, 3, 2, 5, 1, 3, 1, 4, 3, 5, 3, 8, 2, 3, 2, 5, 3, 4, 3, 7, 2, 5, 2, 7, 5, 8, 5, 13, 1, 2, 1, 3, 2, 3, 2, 5, 1, 3, 1, 4, 3, 5, 3, 8, 2, 3, 2, 5, 3, 4, 3, 7, 2, 5, 2, 7, 5, 8, 5, 13, 1, 3, 1, 4, 3, 5, 3
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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[]=1, [p]=p, [p,q]=pq+1, [p,q,r]=pqr+p+r; in general [x_1,...,x_n] = [x_1,...,x_{n-1}]*x_n + [x_1,...,x_{n-2}].
The successive record values in this sequence occur at n=0 and n=2^k-1 for k>1 and are equal to the Fibonacci numbers A000045 (cf. Chrystal, p. 503, Exercise 11).
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REFERENCES
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G. Chrystal, Algebra, Vol. II, pp. 494 ff. (for definition of continuant).
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, Sect. 6.7 (for definition of continuant).
T. Muir, The Theory of Determinants in the Historical Order of Development. 4 vols., Macmillan, NY, 1906-1923, Vol. 2, p. 413 (for definition of continuant).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..4095
T. Muir, The Theory of Determinants in the Historical Order of Development, 4 vols., Macmillan, NY, 1906-1923, Vol. 2.
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PROGRAM
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(ARIBAS) function continuant(n: integer): integer; var len, v, v1, v2, j: integer; begin len := bit_length(n); if len < 2 then v := 1; else v1 := bit_test(n, len-1); v := 1 + bit_test(n, len-1)*bit_test(n, len-2); for j := len-3 to 0 by -1 do v2 := v1; v1 := v; v := v1*bit_test(n, j) + v2; end; end; return v; end; for n := 0 to 102 do write(continuant(n), ", "); end;
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CROSSREFS
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Sequence in context: A066451 A091090 A066075 this_sequence A136107 A124768 A072527
Adjacent sequences: A072344 A072345 A072346 this_sequence A072348 A072349 A072350
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jul 18 2002
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EXTENSIONS
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More terms from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 19 2002
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