|
Search: id:A102310
|
|
|
| A102310 |
|
Square array read by antidiagonals: Fib(k*n). |
|
+0
6
|
|
| 1, 1, 1, 2, 3, 2, 3, 8, 8, 3, 5, 21, 34, 21, 5, 8, 55, 144, 144, 55, 8, 13, 144, 610, 987, 610, 144, 13, 21, 377, 2584, 6765, 6765, 2584, 377, 21, 34, 987, 10946, 46368, 75025, 46368, 10946, 987, 34, 55, 2584, 46368, 317811, 832040, 832040, 317811
(list; table; graph; listen)
|
|
|
OFFSET
|
1,4
|
|
|
FORMULA
|
For prime p, the formula holds: Fib(kp) = Fib(p) * Sum[i=0..floor((k-1)/2), C(k-i-1, i)*(-1)^(ip+i)*Lucas(p)^(k-2i-1) ].
|
|
EXAMPLE
|
1,1,2,3,5,
1,3,8,21,55,
2,8,34,144,610,
3,21,144,987,6765,
5,55,610,6765,75025,
|
|
CROSSREFS
|
Cf. Equals A000045(A003991(k, n)).
Columns include A000045, A001906, A014445, A033888, A102312. Main diagonal is in A054783. Antidiagonal sums are in A102311.
Sequence in context: A085215 A076731 A085216 this_sequence A151546 A117936 A078331
Adjacent sequences: A102307 A102308 A102309 this_sequence A102311 A102312 A102313
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Ralf Stephan, Jan 06 2005
|
|
|
Search completed in 0.002 seconds
|
