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A005378
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The female of a pair of recurrences.
(Formerly M0263)
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7
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1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 16, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 22, 23, 24, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 30, 31, 32, 32, 33, 34, 34, 35, 35, 36, 37, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 43, 44, 45, 45
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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The g.f. (1+z**2+z**4-z**5+z**6)/(z**4+z**3+z**2+z+1)/(z-1)**2 conjectured by Simon Plouffe in his 1992 dissertation is wrong.
F(n) is not equal to M(n) if and only if n+1 is a Fibonacci number (A000045); a(n)=A005379(n)+A192687(n). [Reinhard Zumkeller, Jul 12 2011]
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REFERENCES
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Hofstadter, "Goedel, Escher, Bach", p. 137.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Th. Stoll, On Hofstadter's married functions, Fib. Q., 46/47 (2008/2009), 62-67. - from N. J. A. Sloane, May 30 2009
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 0..10000
_Simon Plouffe_, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
_Simon Plouffe_, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Eric Weisstein's World of Mathematics, Hofstadter Male-Female Sequences.
Index entries for Hofstadter-type sequences
Index entries for sequences from "Goedel, Escher, Bach"
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FORMULA
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F(0) = 1; M(0) = 0; F(n) = n-M(F(n-1)); M(n) = n-F(M(n-1)).
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MATHEMATICA
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f[0] = 1; m[0] = 0; f[n_] := f[n] = n - m[f[n-1]]; m[n_] := m[n] = n - f[m[n-1]]; Table[f[n], {n, 0, 73}]
(* From Jean-François Alcover, Jul 27 2011 *)
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PROG
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(Haskell)
a005378 n = a005378_list !! n
a005378_list = 1 : zipWith (-) [1..] (map a005379 a005378_list)
a005379 n = a005379_list !! n
a005379_list = 0 : zipWith (-) [1..] (map a005378 a005379_list)
-- Without memoization the original recursion would be feasible only for small n.
-- Reinhard Zumkeller, Jul 12 2011
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CROSSREFS
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Cf. A005379.
Sequence in context: A098294 A195119 A077467 * A103355 A029092 A209081
Adjacent sequences: A005375 A005376 A005377 * A005379 A005380 A005381
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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.
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EXTENSIONS
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More terms from James A. Sellers, Jul 12 2000
Comment corrected by Jaroslav Krizek, Dec 25 2011.
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STATUS
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approved
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