|
EXAMPLE
|
First few rows of the array =
n=1 n=2 n=3 n=4 n=5 n=6 n=7 n=8 n=9 n=10 n=11 n=12 n=13 n=14 n=15
r=0: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
r=1: 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, ...
r=2: 1, 1, 3, 1, 5, 3, 7, 1, 7, 5, 13, 3, 13, 7, 15, ...
r=3: 1, 1, 4, 1, 7, 4, 13, 1, 10, 7, 25, 4, 25, 13, 40, ...
r=4: 1, 1, 5, 1, 9, 5, 21, 1, 13, 9, 41, 5, 41, 21, 85, ...
r=5: 1, 1, 6, 1, 11, 6, 31, 1, 16, 11, 61, 6, 61, 31, 156, ...
...
Example: In row 3: (1, 1, 4, 1, 7, 4, 13, ...) = A342633, r = 3.
A342633(7) = 13 = 3*4 + 1. In blocks of 1, 2, 4, 8, ... terms, partial sums are powers of (r+2) = 5: (1, 5, 25, ...).
First few rows of the triangle =
1;
1, 1;
1, 1, 1;
1, 1, 2, 1;
1, 1, 3, 1, 1;
1, 1, 4, 1, 3, 1;
1, 1, 5, 1, 5, 2, 1;
1, 1, 6, 1, 7, 3, 3, 1;
1, 1, 7, 1, 9, 4, 7, 1, 1;
1, 1, 8, 1, 11, 5, 13, 1, 4, 1;
1, 1, 9, 1, 13, 6, 21, 1, 7, 3, 1;
1, 1, 10, 1, 15, 7, 31, 1, 10, 5, 5, 1;
1, 1, 11, 1, 17, 8, 43, 1, 13, 7, 13, 2, 1;
1, 1, 12, 1, 19, 9, 57, 1, 16, 9, 21, 3, 5, 1;
1, 1, 13, 1, 21, 11, 73, 1, 19, 11, 31, 4, 13, 2, 1;
...
|