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

0,12

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

Links

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

Formula

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

Example

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...

Mathematica

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

Crossrefs

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

Sequence in context: A236533 A298187 A298183 * A298167 A298957 A298902

Adjacent sequences: A098353 A098354 A098355 * A098357 A098358 A098359

Keyword

nonn,tabl,easy

Author

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

Status

approved