A005210 a(n) = |a(n-1) + 2a(n-2) - n|. (Formerly M0400)

1, 1, 0, 2, 3, 1, 0, 6, 3, 5, 0, 2, 11, 1, 8, 6, 5, 1, 8, 10, 5, 3, 10, 8, 3, 7, 14, 0, 1, 29, 0, 26, 7, 25, 4, 18, 11, 9, 8, 14, 11, 3, 18, 20, 11, 5, 20, 18, 9, 5, 28, 14, 17, 9, 12, 26, 7, 1, 44, 14, 41, 7, 26, 24, 11, 7, 38, 16, 23, 15, 10, 32, 21, 11, 22, 32, 1, 13, 64, 10, 57, 5, 36, 38, 25, 15, 22, 36

Offset

1,4

Comments

It seems likely that every number will eventually appear.

References

Popular Computing (Calabasas, CA), Z-Sequences, Vol. 4 (No. 42, Sep 1976), pp. 12-16.

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

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..20000 (first 1000 terms from T. D. Noe)

Popular Computing (Calabasas, CA), Z-Sequences, continued. Annotated and scanned copy of pages 14, 15, 16, 18 of Vol. 5 (No. 56, Nov 1977).

J. Shallit, Letter to N. J. A. Sloane Mar 14, 1979, concerning A001787, A005209, A005210, A005211

Maple

f:=proc(n) option remember;
if n <= 1 then 1 else abs(2*f(n-2)+f(n-1)-n); fi; end;
[seq(f(n), n=1..60)]; # N. J. A. Sloane, Apr 16 2015

Mathematica

RecurrenceTable[{a[1]==a[2]==1, a[n]==Abs[a[n-1]+2a[n-2]-n]}, a, {n, 90}] (* Harvey P. Dale, Mar 23 2012 *)

Prog

(Haskell)
a005210 n = a005210_list !! (n-1)
a005210_list = 1 : 1 : (zipWith ((abs .) . (-))
    [3..] $ zipWith (+) (tail a005210_list) (map (2 *) a005210_list))
-- Reinhard Zumkeller, Aug 11 2014

Crossrefs

Record values and where they occur: A005211 and A242014.

Zeros: A051202. Consecutive equal terms: A256962.

Least inverse: A051203.

Sequence in context: A352366 A264428 A256550 * A352363 A264430 A264433

Adjacent sequences: A005207 A005208 A005209 * A005211 A005212 A005213

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from David W. Wilson

Status

approved