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A005378 The female of a pair of recurrences.
(Formerly M0263)
8
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)
OFFSET

0,3

COMMENTS

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]

Differs from A098294 in indices n=0,17,20,22,25,27,29,30,... - M. F. Hasler, Jun 29 2014

REFERENCES

Hofstadter, "Goedel, Escher, Bach", p. 137.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

D. R. Hofstadter, Eta-Lore [Cached copy, with permission]

D. R. Hofstadter, Pi-Mu Sequences [Cached copy, with permission]

D. R. Hofstadter and N. J. A. Sloane, Correspondence, 1977 and 1991

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Th. Stoll, On Hofstadter's married functions, Fib. Q., 46/47 (2008/2009), 62-67. - from N. J. A. Sloane, May 30 2009

Eric Weisstein's World of Mathematics, Hofstadter Male-Female Sequences.

Index entries for Hofstadter-type sequences

Index entries for sequences from "Goedel, Escher, Bach"

FORMULA

F(0) = 1; M(0) = 0; F(n) = n-M(F(n-1)); M(n) = n-F(M(n-1)).

MATHEMATICA

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}] (* Jean-François Alcover, Jul 27 2011 *)

PROG

(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

CROSSREFS

Cf. A005379.

Sequence in context: A098294 A195119 A077467 * A247911 A103355 A029092

Adjacent sequences:  A005375 A005376 A005377 * A005379 A005380 A005381

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from James A. Sellers, Jul 12 2000

Comment corrected by Jaroslav Krizek, Dec 25 2011

STATUS

approved

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Last modified November 23 09:53 EST 2014. Contains 249840 sequences.