%I A116192
%S A116192 1,3,3,5,4,5,7,7,7,7,9,8,8,8,9,11,11,10,10,11,11,13,12,13,12,13,12,13,
%T A116192 15,15,15,15,15,15,15,15,17,16,16,16,16,16,16,16,17,19,19,18,18,18,18,
%U A116192 18,18,19,19,21,20,21,20,20,20,20,20,21,20,21,23,23,23,23,22,22,22,22
%N A116192 Triangle T(n,k), 0<=k<=n : T(n,k)is smallest number such that T(n,k)>
               T(n-1,k-1), T(n,k)>T(n-1,k), T(n,k)and T(n-1,k-1)+T(n-1,k) have the 
               same parity, T(0,0)=1 .
%C A116192 Sequence read mod 2 gives A047999 .
%F A116192 Sum_{k, 0<=k<=n}T(n,k)=A128806(n). T(2n,n)=A008574(n). T(n,k)=2n+1 if 
               binomial(n,k) is odd, T(n,k)=2n if binomial(n,k) is even .
%e A116192 Triangle begins:
%e A116192 1;
%e A116192 3, 3;
%e A116192 5, 4, 5;
%e A116192 7, 7, 7, 7;
%e A116192 9, 8, 8, 8, 9;
%e A116192 11, 11, 10, 10, 11, 11;
%e A116192 13, 12, 13, 12, 13, 12, 13;
%e A116192 15, 15, 15, 15, 15, 15, 15, 15 ;...
%Y A116192 Diagonals : A005408, A014601.
%Y A116192 Sequence in context: A008316 A072820 A131950 this_sequence A090104 A075795 
               A058268
%Y A116192 Adjacent sequences: A116189 A116190 A116191 this_sequence A116193 A116194 
               A116195
%K A116192 nonn,tabl
%O A116192 0,2
%A A116192 Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 08 2007