A066949 Take the sum of the previous two terms, subtract n if this sum is greater than n.

0, 1, 1, 2, 3, 5, 2, 7, 1, 8, 9, 6, 3, 9, 12, 6, 2, 8, 10, 18, 8, 5, 13, 18, 7, 25, 6, 4, 10, 14, 24, 7, 31, 5, 2, 7, 9, 16, 25, 2, 27, 29, 14, 43, 13, 11, 24, 35, 11, 46, 7, 2, 9, 11, 20, 31, 51, 25, 18, 43, 1, 44, 45, 26, 7, 33, 40, 6, 46, 52, 28, 9, 37, 46, 9, 55, 64, 42, 28, 70, 18

Offset

0,4

Links

T. D. Noe, Table of n, a(n) for n = 0..10000

Formula

a(n) = a(n-1)+a(n-2)-n if a(n-1)+a(n-2)>n, a(n) = a(n-1)+a(n-2) otherwise; a(0) = 0, a(1) = 1.

Mathematica

a[0] = 0; a[1] = 1; a[n_] := a[n] = Block[ {b = a[n - 1] + a[n - 2]}, If[b > n, Return[b - n], Return[b]]]; Table[a[n], {n, 0, 80} ]
nxt[{n_, a_, b_}]:={n+1, b, If[a+b>n+1, a+b-n-1, a+b]}; Transpose[ NestList[ nxt, {1, 0, 1}, 80]][[2]] (* Harvey P. Dale, Sep 04 2013 *)

Prog

(Haskell)
a066949 n = a066949_list !! n
a066949_list = 0 : 1 : f 2 1 0 where
   f k x x' | z > k     = (z - k) : f (k+1) (z - k) x
            | otherwise = z : f (k+1) z x where z = x + x'
-- Reinhard Zumkeller, Oct 17 2011
(Python)
l=[0, 1]
for n in range(2, 101):
    x=l[n - 1] + l[n - 2]
    if x>n: l.append(x - n)
    else: l.append(x)
print(l) # Indranil Ghosh, Jun 03 2017

Crossrefs

Cf. A000045.

Sequence in context: A201652 A359609 A272636 * A073481 A178094 A364874

Adjacent sequences: A066946 A066947 A066948 * A066950 A066951 A066952

Keyword

easy,nonn,nice

Author

Floor van Lamoen, Jan 25 2002

Extensions

Edited by Robert G. Wilson v, Jan 31 2002

Status

approved