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A035505 Active part of Kimberling's expulsion array as a triangular array. 2

%I

%S 4,2,6,2,7,4,8,7,9,2,10,6,6,2,11,9,12,7,13,8,13,12,8,9,14,11,15,2,16,

%T 6,2,11,16,14,6,9,17,8,18,12,19,13,18,17,12,9,19,6,13,14,20,16,21,11,

%U 22,2,16,14,21,13,11,6,22,19,2,9,23,12,24,17,25,18,23,2,12,19,24,22,17,6

%N Active part of Kimberling's expulsion array as a triangular array.

%C Active or shuffle part of Kimberling's expulsion array (A035486) is given by the elements K(i,j), where j<2*i-3 [From _Enrique Pérez Herrero_, Apr 14 2010]

%D R. K. Guy, Unsolved Problems Number Theory, Sect. E35.

%D C. Kimberling, Problem 1615, Crux Mathematicorum, Vol. 17 (2) 44 1991 and Vol. 18, March 1992, p. 82-83.

%H E. Pérez Herrero, <a href="/A035505/b035505.txt">Table of n, a(n) for n=1..10000</a>

%F From _Enrique Pérez Herrero_, Apr 14 2010: (Start)

%F a(n)=K(A000194(n)+2,A074294(n)), where:

%F K(i,j)=i+j-1; (j>=2*i-3)

%F K(i,j)=K(i-1,i-(j+2)/2); If j is Even and (j<2*i-3)

%F K(i,j)=K(i-1,i+(j-1)/2); If j is Odd and (j<2*i-3) (End)

%e 4 2; 6 2 7 4; 8 7 9 2 10 6; ...

%t Contribution from _Enrique Pérez Herrero_, Apr 14 2010: (Start)

%t A000194[n_] := Floor[(1 + Sqrt[4 n - 3])/2];

%t A074294[n_] := n - 2*Binomial[Floor[1/2 + Sqrt[n]], 2];

%t K[i_, j_] := i + j - 1 /; (j >= 2 i - 3);

%t K[i_, j_] := K[i - 1, i - (j + 2)/2] /; (EvenQ[j] && (j < 2 i - 3));

%t K[i_, j_] := K[i - 1, i + (j - 1)/2] /; (OddQ[j] && (j < 2 i - 3));

%t A035505[n_] := K[A000194[n] + 2, A074294[n]] (End)

%Y Cf. A006852, A007063, A038807, A035486.

%Y A175312,A074294,A000194,A006852,A007063 [From _Enrique Pérez Herrero_, Apr 14 2010]

%K nonn,tabf,nice,easy

%O 1,1

%A _N. J. A. Sloane_.

%E More terms from _James A. Sellers_, Dec 23 1999

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Last modified February 22 18:05 EST 2019. Contains 320400 sequences. (Running on oeis4.)