OFFSET
1,1
COMMENTS
Active or shuffle part of Kimberling's expulsion array (A035486) is given by the elements K(i,j), where j < 2*i-3. [Enrique Pérez Herrero, Apr 14 2010]
REFERENCES
R. K. Guy, Unsolved Problems Number Theory, Sect. E35.
LINKS
Enrique Pérez Herrero, Table of n, a(n) for n = 1..10000
Clark Kimberling, Problem 1615, Crux Mathematicorum, Vol. 17 (2) 44 1991; Solution to Problem 1615, Crux Mathematicorum, Vol. 18, March 1992, p. 82-83.
FORMULA
From Enrique Pérez Herrero, Apr 14 2010: (Start)
K(i,j) = i + j - 1; (j >= 2*i - 3)
K(i,j) = K(i-1, i-(j+2)/2) if j is even and j < 2*i - 3
K(i,j) = K(i-1, i+(j-1)/2); if j is odd and j < 2*i - 3.
(End)
EXAMPLE
4 2; 6 2 7 4; 8 7 9 2 10 6; ...
MATHEMATICA
A000194[n_] := Floor[(1 + Sqrt[4 n - 3])/2];
A074294[n_] := n - 2*Binomial[Floor[1/2 + Sqrt[n]], 2];
K[i_, j_] := i + j - 1 /; (j >= 2 i - 3);
K[i_, j_] := K[i - 1, i - (j + 2)/2] /; (EvenQ[j] && (j < 2 i - 3));
K[i_, j_] := K[i - 1, i + (j - 1)/2] /; (OddQ[j] && (j < 2 i - 3));
(* Enrique Pérez Herrero, Apr 14 2010 *)
CROSSREFS
KEYWORD
nonn,tabf,nice,easy
AUTHOR
EXTENSIONS
More terms from James A. Sellers, Dec 23 1999
STATUS
approved