OFFSET
0,4
COMMENTS
The array P =
1, 0, 0, 0, 0, 0, ...
0, 1, 0, 0, 0, 0, ...
0, 1, 1, 0, 0, 0, ...
0, 0, 2, 1, 0, 0, ...
0, 0, 1, 3, 1, 0, ...
0, 0, 0, 3, 4, 1, ...
...
... as shown on page 107 of "A Primer for the Fibonacci Numbers".
The array A is composed of arithmetic sequences, as a matrix.
1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, ...
1, 3, 5, 7, 9, ...
1, 4, 7, 10, 13, ...
1, 5, 9, 13, 17, ...
...
Leftmost column = Fibonacci numbers, next column (1, 2, 5, 10, 20, ...) = Fibonacci numbers convolved with themselves.
REFERENCES
V. E. Hoggatt, Jr., editor; "A Primer for the Fibonacci Numbers", 1963, p. 107.
FORMULA
Let P = an array with columns composed of Pascal's Triangle rows, offset, spaces filled in with zeros; A = an array composed of arithmetic sequences(n, k). Perform P * A and extract antidiagonals which become the rows of A106196.
EXAMPLE
The operation P * A generates the array:
1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, ...
2, 5, 8, 11, 14, ...
3, 10, 17, 24, 31, ...
5, 20, 35, 50, 65, ...
...
from which we extract antidiagonals, read by rows, become triangle A106196:
1;
1, 1;
2, 2, 1;
3, 5, 3, 1;
5, 10, 8, 4, 1;
8, 20, 17, 11, 5, 1;
13, 38, 35, 24, 14, 6, 1;
21, 71, 68, 50, 31, 17, 7, 1;
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Apr 24 2005
STATUS
approved