OFFSET
1,4
COMMENTS
Row sums = A001519, the odd-indexed Fibonacci numbers starting (1, 2, 5, 13, 34, ...).
Sum of n-th row terms = rightmost term of next row.
FORMULA
Triangle read by rows, M*Q. M = an infinite lower triangular matrix with (1, 1, 2, 4, 8, 16, ...) in every column and Q = a matrix (1, 1, 2, 5, 13, 34, ...) as the main diagonal and the rest zeros.
Let M = production matrix for reversed rows of the triangle as follows:
1, 1;
1, 0, 2;
1, 0, 0, 2;
1, 0, 0, 0, 2;
1, 0, 0, 0, 0, 2;
...
Reversal of n-th row of triangle A152251 = top row terms of M^(n-1). Example: top row of M^3 = (5, 2, 2, 4). - Gary W. Adamson, Jul 07 2011
EXAMPLE
First few rows of the triangle =
1;
1, 1;
2, 1, 2;
4, 2, 2, 5;
8, 4, 4, 5, 13;
16, 8, 8, 10, 13, 34;
32, 16, 16, 20, 26, 34, 89;
64, 32, 32, 40, 52, 68, 89, 233;
128, 64, 64, 80, 104, 136, 178, 233, 610;
...
Row 4 = (8, 4, 4, 5, 13) = termwise products of (8, 4, 2, 1, 1) and (1, 1, 2, 5, 13).
CROSSREFS
KEYWORD
AUTHOR
Gary W. Adamson, Nov 30 2008
EXTENSIONS
Last term corrected by Olivier Gérard, Aug 11 2016
STATUS
approved