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Lexicographically least permutation of the integers in a triangle satisfying T(n,k) + T(n+1,k) <= T(n+1,k+1).
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%I #16 May 11 2013 12:31:04

%S 1,2,3,4,6,9,5,10,16,25,7,12,22,38,63,8,15,27,49,87,150,11,19,34,61,

%T 110,197,347,13,24,43,77,138,248,445,792,14,28,52,95,172,310,558,1003,

%U 1795,17,31,59,111,206,378,688,1246,2249,4044,18,35,66,125,236,442,820,1508,2754,5003,9047,20,39,74,140,265,501,943,1763

%N Lexicographically least permutation of the integers in a triangle satisfying T(n,k) + T(n+1,k) <= T(n+1,k+1).

%C Apparently, T(n,k) ~ n*2^k as n grows.

%H Paul Tek, <a href="/A185290/b185290.txt">Table of n, a(n) for n = 1..10000</a>

%e The first rows are:

%e [1]

%e [2,3]

%e [4,6,9]

%e [5,10,16,25]

%e For T(1,1), we choose the first integer not yet used: 1.

%e For T(2,1), we choose the first integer not yet used: 2.

%e For T(2,2), we choose the first integer >= T(1,1)+T(2,1) not yet used: 3.

%e For T(3,1), we choose the first integer not yet used: 4.

%e For T(3,2), we choose the first integer >= T(2,1)+T(3,1) not yet used: 6.

%e For T(3,3), we choose the first integer >= T(2,2)+T(3,2) not yet used: 9.

%e etc.

%Y Cf. A035312.

%K nonn,tabl

%O 1,2

%A _Paul Tek_, Apr 23 2013