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 give A002620. - 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; then lim_{n->infinity} 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) = 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
KEYWORD
easy,nonn,tabf
AUTHOR
Franklin T. Adams-Watters, Aug 25 2006
STATUS
approved