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 A102310 Square array read by antidiagonals: Fibonacci(k*n). 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, 46368, 2584, 55 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 REFERENCES R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. 2nd Edition. Addison-Wesley, Reading, MA, 1994, p. 294. LINKS Freddy Barrera, Antidiagonals n = 1..50, flattened FORMULA For prime p, the formula holds: Fibonacci(k*p) = Fibonacci(p) * Sum_{i=0..floor((k-1)/2)} C(k-i-1, i)*(-1)^(i*p+i)*Lucas(p)^(k-2i-1). A(n, k) = F((n-1)*k)*F(k+1) + F((n-1)*k-1)*F(k), where F(n) = A000045(n). - Freddy Barrera, Jun 24 2019 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-François Alcover, Jun 10 2017 *) PROG (Sage) F = fibonacci # A000045 def A(n, k):     return F((n-1)*k)*F(k+1) + F((n-1)*k - 1)*F(k) [A(n, k) for d in (1..10) for n, k in zip((d..1, step=-1), (1..d))] # Freddy Barrera, Jun 24 2019 (MAGMA) /* As triangle */ [[Fibonacci(k*(n-k+1)): k in [1..n]]: n in [1.. 15]]; // Vincenzo Librandi, Jul 04 2019 CROSSREFS 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: A341653 A085216 A300663 * 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 June 13 18:45 EDT 2021. Contains 345008 sequences. (Running on oeis4.)