A124801 Triangle, row sums = Fibonacci numbers in two ways.

1, 1, 0, 1, 0, 1, 1, 0, 3, -1, 1, 0, 6, -4, 1, 1, 0, 10, -10, 10, -3, 1, 0, 15, -20, 30, -18, 5, 1, 0, 21, -35, 70, -63, 35, -8, 1, 0, 28, -56, 140, -168, 140, -64, 13

Offset

1,9

Comments

n-th row sum of signed terms = Fn; n-th row sum of unsigned terms = F(2n-3).

Links

Table of n, a(n) for n=1..45.

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

Cf. A039834, A124802.

Sequence in context: A287822 A162169 A216954 * A124926 A175946 A115378

Adjacent sequences: A124798 A124799 A124800 * A124802 A124803 A124804

Keyword

tabl,sign

Author

Gary W. Adamson, Nov 08 2006

Status

approved