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EXAMPLE
| Triangle begins:
1;
1, 1;
2, 2, 1, 1;
6, 6, 4, 4, 2, 2, 1;
25, 25, 19, 19, 13, 13, 9, 5, 5, 3, 1, 1;
138, 138, 113, 113, 88, 88, 69, 50, 50, 37, 24, 24, 15, 10, 5, 5, 2, 1;
970, 970, 832, 832, 694, 694, 581, 468, 468, 380, 292, 292, 223, 173, 123, 123, 86, 62, 38, 38, 23, 13, 8, 3, 3, 1;
8390, 8390, 7420, 7420, 6450, 6450, 5618, 4786, 4786, 4092, 3398, 3398, 2817, 2349, 1881, 1881, 1501, 1209, 917, 917, 694, 521, 398, 275, 275, 189, 127, 89, 51, 51, 28, 15, 7, 4, 1, 1;
There are A135901(n) number of terms in row n.
To generate the triangle, start with a single 1 in row 0,
and then obtain row n+1 from row n by inserting zeros at
positions {[(m+3)^2/4 - 2], m=0,1,2,...} and then
taking reverse partial sums (i.e., summing from right to left).
Start with row 0, insert a zero in front of the '1' at position 0:
[0,1];
take reverse partial sums to get row 1:
[1,1];
insert zeros at positions [0,2]:
[0,1,0,1];
take reverse partial sums to get row 2:
[2,2,1,1];
insert zeros at positions [0,2,4]:
[0,2,0,2,0,1,1];
take reverse partial sums to get row 3:
[6,6,4,4,2,2,1];
insert zeros at positions [0,2,4,7]:
[0,6,0,6,0,4,4,0,2,2,0,1];
take reverse partial sums to get row 4:
[25,25,19,19,13,13,9,5,5,3,1,1];
insert zeros at positions [0,2,4,7,10,14]:
[0,25,0,25,0,19,19,0,13,13,0,9,5,5,0,3,1,1];
take reverse partial sums to get row 5:
[138,138,113,113,88,88,69,50,50,37,24,24,15,10,5,5,2,1].
Triangle A135880 begins:
1;
1, 1;
2, 2, 1;
6, 7, 3, 1;
25, 34, 15, 4, 1;
138, 215, 99, 26, 5, 1;
970, 1698, 814, 216, 40, 6, 1; ...
and is generated by matrix powers of itself.
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