A124731 - OEIS

%I #6 Mar 03 2013 13:48:18

%S 1,2,1,4,3,2,8,7,10,2,16,15,34,12,4,32,31,98,46,32,4,64,63,258,144,

%T 156,36,8,128,127,642,402,600,192,88,8,256,255,1538,1044,2004,792,560,

%U 96,16

%N Triangle, row sums = powers of 3, companion to A124730.

%C In A124730, the diagonals are switched. Row sums are powers of 3 in both triangles.

%F Let M = the infinite bidiagonal matrix with (2,1,2,1...) in the main diagonal and (1,2,1,2...) in the subdiagonal. Extracting finite n X n matrices of this form, we take M^n * [1,0,0,0...].

%e Row 2 = (4, 3, 2) since (using the 3 X 3 matrix m = [2,0,0; 1,1,0; 0,2,2]), m^2 * [1,0,0] = [4,3,2].

%e First few rows of the triangle are:

%e 1;

%e 2, 1;

%e 4, 3, 2;

%e 8, 7, 10, 2;

%e 16, 15, 34, 12, 4;

%e 32, 31, 98, 46, 32, 4;

%e 64, 63, 258, 144, 156, 36, 8;

%e ...

%Y Cf. A124730, A124732.

%K nonn,tabl

%O 0,2

%A _Gary W. Adamson_ & _Roger L. Bagula_, Nov 05 2006