A098356 Multiplication table of the Fibonacci numbers read by antidiagonals.

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 2, 0, 0, 3, 2, 2, 3, 0, 0, 5, 3, 4, 3, 5, 0, 0, 8, 5, 6, 6, 5, 8, 0, 0, 13, 8, 10, 9, 10, 8, 13, 0, 0, 21, 13, 16, 15, 15, 16, 13, 21, 0, 0, 34, 21, 26, 24, 25, 24, 26, 21, 34, 0, 0, 55, 34, 42, 39, 40, 40, 39, 42, 34, 55, 0, 0, 89, 55, 68, 63, 65, 64, 65

Offset: 0

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Sep 04 2004

Keywords

• nonn
• tabl
• easy

Comments

Same as triangle T(n,k) = F(n)-F(k)*F(n-k+1), read by rows, F(i) = A000045(i). - Dale Gerdemann, Apr 24 2016

Examples

			Table begins:
   0   0   0   0   0   0   0   0   0 ...
   0   1   1   2   3   5   8  13  21...
   0   1   1   2   3   5   8  13  21...
   0   2   2   4   6  10  16  26  42...
   0   3   3   6   9  15  24  39  63...
   0   5   5  10  15  25  40  65 105...
   0   8   8  16  24  40  64 104 168...
   0  13  13  26  39  65 104 169 273...
   0  21  21  42  63 105 168 273 441...
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..11324 (rows 0 <= n <= 149, flattened)

Crossrefs

Cf. A003991, A058071, A001629 (antidiagonal sums).

Programs

Mathematica

Table[Fibonacci[n] - Fibonacci[k]*Fibonacci[n - k + 1], {n, 13}, {k, n}] // Flatten (* Michael De Vlieger, Dec 11 2020 *)

Formula

T(n,k) = T(k,n) = A000045(n)*A000045(k) = A143211(n,k). - R. J. Mathar, Dec 11 2020