cp's OEIS Frontend

A165162 Triangle T(n,m) with 2n-1 entries per row, read by rows: the first n entries count down from n to 1, the remaining n-1 entries down from n-1 to 1.

%I A165162 #7 Aug 02 2012 08:34:15
%S A165162 1,2,1,1,3,2,1,2,1,4,3,2,1,3,2,1,5,4,3,2,1,4,3,2,1,6,5,4,3,2,1,5,4,3,
%T A165162 2,1,7,6,5,4,3,2,1,6,5,4,3,2,1,8,7,6,5,4,3,2,1,7,6,5,4,3,2,1,9,8,7,6,
%U A165162 5,4,3,2,1,8,7,6,5,4,3,2,1,10,9,8,7,6,5,4,3,2,1,9,8,7,6,5,4,3,2,1
%N A165162 Triangle T(n,m) with 2n-1 entries per row, read by rows: the first n entries count down from n to 1, the remaining n-1 entries down from n-1 to 1.
%C A165162 Arose in a study of saddle-point quantities (see A057058 and references therein).
%C A165162 In conjunction with denominators defined in A165200 this constitutes a triangle of fractions:
%C A165162 1;
%C A165162 2,1/2,1/4;
%C A165162 3,2/2,1/3,2/6,1/9;
%C A165162 4,3/2,2/3,1/4,3/8,2/12,1/16;
%D A165162 P. Curtz, Stabilite locale des systemes quadratiques. Ann. sc. Ecole Normale Sup., 1980, 293-302.
%F A165162 T(n,m) = n-m+1 for 1 <= m <= n. T(n,m) = 2n-m for n< m <= 2n-1. [R. J. Mathar, Nov 24 2010]
%F A165162 sum_{m=1..2n-1} T(n,m) = n^2.
%e A165162 1;
%e A165162 2,1,1;
%e A165162 3,2,1,2,1;
%e A165162 4,3,2,1,3,2,1;
%e A165162 5,4,3,2,1,4,3,2,1;
%t A165162 Flatten[ Table[ Range[k, 1, -1], {n, 1, 10}, {k, {n, n-1}}]] (* _Jean-François Alcover_, Aug 02 2012 *)
%K A165162 nonn,easy,tabf
%O A165162 1,2
%A A165162 _Paul Curtz_, Sep 06 2009