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EXAMPLE
| Triangle T begins:
1;
1, 1;
4, 2, 1;
18, 6, 3, 1;
96, 28, 8, 4, 1;
580, 150, 40, 10, 5, 1;
3852, 930, 216, 54, 12, 6, 1;
27678, 6286, 1386, 294, 70, 14, 7, 1;
212224, 46120, 9552, 1960, 384, 88, 16, 8, 1;
1722312, 359946, 71820, 13770, 2664, 486, 108, 18, 9, 1;
14685140, 2973650, 571440, 106290, 19060, 3510, 600, 130, 20, 10, 1; ...
Illustrate recurrence by products of row and column vectors:
T(4,1) = [8,4,1]*[1,3,8]~ = 8*1 + 4*3 + 1*8 = 28;
T(6,0) = [930,216,54,12,6,1]*[1,2,6,28,150,930]~ = 3852;
T(7,1) = [6286,1386,294,70,14,7,1]*[1,2,6,28,150,930,6286]~ = 27678.
Matrix square T^2 begins:
1;
2, 1;
10, 4, 1;
54, 18, 6, 1;
324, 96, 28, 8, 1;
2130, 580, 150, 40, 10, 1;
15102, 3852, 930, 216, 54, 12, 1;
114282, 27678, 6286, 1386, 294, 70, 14, 1; ...
which equals T shifted right one column with the secondary diagonal dropped.
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