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 A122196 Fractal sequence: count down by 2's from successive integers. 10
 1, 2, 3, 1, 4, 2, 5, 3, 1, 6, 4, 2, 7, 5, 3, 1, 8, 6, 4, 2, 9, 7, 5, 3, 1, 10, 8, 6, 4, 2, 11, 9, 7, 5, 3, 1, 12, 10, 8, 6, 4, 2, 13, 11, 9, 7, 5, 3, 1, 14, 12, 10, 8, 6, 4, 2, 15, 13, 11, 9, 7, 5, 3, 1, 16, 14, 12, 10, 8, 6, 4, 2, 17, 15, 13, 11, 9, 7, 5, 3, 1, 18, 16, 14, 12, 10, 8, 6, 4, 2, 19, 17 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS First differences of A076644. Fractal - deleting the first occurrence of each integer leaves the original sequence. Also, original sequence plus 1. 1's occur at square indices. New values occur at indices m^2+1 and m^2+m+1. Ordinal transform of A122197. Row sums = A002620: (1, 2, 4, 6, 9, 12, 16, 20,...). - Gary W. Adamson, Nov 29 2008 From Gary W. Adamson, Dec 05 2009: (Start) A122196 considered as an infinite lower triangular matrix * [1,2,3,...] = A006918 starting (1, 2, 5, 8, 14, 20, 30, 40,...). Let A122196 = an infinite lower triangular matrix M. Lim_{n=1..inf.} M^n = A171238, a left-shifted vector considered as a matrix. (End) A122196 is the fractal sequence associated with the dispersion A082156; that is, A122196(n) is the number of the row of A082156 that contains n.  - Clark Kimberling, Aug 12 2011 From Johannes W. Meijer, Sep 09 2013: (Start) The alternating row sums lead to A004524(n+2). The antidiagonal sums equal A001840(n). (End) LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA From Boris Putievskiy, Sep 09 2013: (Start) a(n) = 2*(1-A122197(n)) + A000267(n-1). a(n) = floor(sqrt(4*n-1))-2*((n-1) mod (t+1)), where t = floor((sqrt(4*n-3)-1)/2). (End) From Johannes W. Meijer, Sep 09 2013: (Start) T(n, k) = n - 2*k + 2, for n >= 1 and 1 <= k <= floor((n+1)/2). T(n, k) = A002260(n, n-2*k+2) (End) EXAMPLE The first few rows of the sequence a(n) as a triangle T(n, k): n/k  1   2   3 1    1 2    2 3    3,  1 4    4,  2 5    5,  3,  1 6    6,  4,  2 MAPLE From Johannes W. Meijer, Sep 09 2013: (Start) a := proc(n) local t: t:=floor((sqrt(4*n-3)-1)/2): floor(sqrt(4*n-1))-2*((n-1) mod (t+1)) end: seq(a(n), n=1..92); # End first program. T := (n, k) -> n-2*k+2: seq(seq(T(n, k), k=1..floor((n+1)/2)), n=1..18); # End second program. (End) MATHEMATICA Flatten@Range[Range[10], 1, -2] (* Birkas Gyorgy, Apr 07 2011 *) PROG (Haskell) a122196 n = a122196_list !! (n-1) a122196_list = concatMap (\x -> enumFromThenTo x (x - 2) 1) [1..] -- Reinhard Zumkeller, Jul 19 2012 CROSSREFS Cf. A076644, A122197, A000290, A033638, A002620, A006918, A171238, A082156, A000267. Sequence in context: A286001 A304106 A022446 * A023117 A023127 A125159 Adjacent sequences:  A122193 A122194 A122195 * A122197 A122198 A122199 KEYWORD easy,nonn,tabf AUTHOR Franklin T. Adams-Watters, Aug 25 2006 STATUS approved

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Last modified January 24 03:56 EST 2019. Contains 319412 sequences. (Running on oeis4.)