A070867 a(1) = a(2) = 1; a(n) = a(n-1 - a(n-1)) + a(n-1 - a(n-2)).

1, 1, 2, 2, 2, 4, 3, 4, 4, 4, 8, 5, 5, 8, 8, 6, 8, 12, 8, 11, 9, 9, 10, 13, 16, 9, 12, 20, 10, 12, 23, 12, 15, 21, 13, 17, 18, 19, 19, 22, 21, 19, 19, 26, 28, 16, 24, 33, 21, 26, 23, 36, 16, 26, 39, 16, 30, 33, 36, 19, 34, 31, 43, 23, 30, 32, 38, 23, 40, 26, 38, 43, 31, 31, 38, 44

Offset

1,3

References

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 129.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Nick Hobson, Python program for this sequence

Eric Weisstein's World of Mathematics, Wolfram Sequences

Index entries for Hofstadter-type sequences

Formula

a(n) = a(n-1 - a(n-1)) + a(n-1 - a(n-2)), with a(1) = a(2) = 1.

Mathematica

a[1]=a[2]=1; a[n_]:= a[n]= a[n-1 -a[n-1]] + a[n-1 -a[n-2]]; Table[a[n], {n, 80}]

Prog

(Haskell)
a070867 n = a070867_list !! (n-1)
a070867_list = 1 : 1 : zipWith (+)
   (map a070867 $ zipWith (-) [2..] a070867_list)
   (map a070867 $ zipWith (-) [2..] $ tail a070867_list)
-- Reinhard Zumkeller, May 31 2013
(Sage)
@CachedFunction
def a(n): # A070867
    if (n<3): return 1
    else: return  a(n-1 -a(n-1)) + a(n-1 -a(n-2))
[a(n) for n in (1..80)] # G. C. Greubel, Mar 28 2022

Crossrefs

Cf. A005185, A226222.

Sequence in context: A166008 A194291 A194323 * A241164 A029157 A247301

Adjacent sequences: A070864 A070865 A070866 * A070868 A070869 A070870

Keyword

nonn,easy

Author

N. J. A. Sloane, May 19 2002

Extensions

More terms from John W. Layman, May 21 2002

Erroneous comma in sequence corrected by Nick Hobson, Feb 17 2007

Status

approved