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A102310 Square array read by antidiagonals: Fib(k*n). 5
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, 46368, 2584, 55 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..55.

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,

MATHEMATICA

Table[Fibonacci[k*(n-k+1)], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-Fran├žois Alcover, Jun 10 2017 *)

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 * A151546 A117936 A264766

Adjacent sequences:  A102307 A102308 A102309 * A102311 A102312 A102313

KEYWORD

nonn,tabl

AUTHOR

Ralf Stephan, Jan 06 2005

STATUS

approved

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Last modified February 22 19:36 EST 2018. Contains 299469 sequences. (Running on oeis4.)