OFFSET
1,9
COMMENTS
n-th row sum of signed terms = Fn; n-th row sum of unsigned terms = F(2n-3).
FORMULA
Diagonalize the inverse binomial transform of the Fibonacci sequence as an infinite matrix, M; and P = Pascal's triangle as an infinite lower triangular matrix. The triangle A124802 = P*M, with the zeros deleted.
EXAMPLE
A039834, (1, 0, 1, -1, 2, -3, 5, -8, 13...) = the diagonal of M, then the first few rows of P*M =
1;
1, 0;
1, 0, 1;
1, 0, 3, -1;
1, 0, 6, -4, 2;
1, 0, 10, -10, 10, -3;
1, 0, 15, -20, 30, -18, 5;
1, 0, 21, -35, 70, -63, 35, -8;
...
Row 7 terms (signed) = F7 = 13 = (1 + 15 -20 + 30 - 18 + 5).
Row 7 terms (unsigned) = F11 = 28 = (1 + 15 + 20 + 30 + 18 + 5).
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Gary W. Adamson, Nov 08 2006
STATUS
approved