A097082 Number of permutations p of (1,2,3,...,n) such that k+p(k) is a Fibonacci number for 1 <= k <= n.
1, 1, 1, 1, 2, 1, 2, 4, 2, 1, 4, 4, 20, 4, 5, 1, 20, 24, 8, 96, 200, 24, 4, 25, 1, 3, 200, 48, 288, 48, 64, 2304, 1600, 10800, 288, 432, 8, 675, 650, 1, 26, 9, 10400, 1600, 576, 2304, 23040, 576, 2560, 1024, 368640, 516096, 128000, 2240000, 5832000, 32256, 2304, 46656, 64, 96, 91125, 3750, 84500, 6, 1, 676, 9, 261
Offset: 0
Keywords
Programs
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Mathematica
nmax=67; A010056[n_]:=With[{fibs=Fibonacci[Range[nmax]]}, If[MemberQ[fibs, n], 1, 0]]; a[n_]:=Permanent[Table[If[A010056[i+j]==1,1,0],{i,n},{j,n}]]; Join[{1},Array[a,nmax]] (* Stefano Spezia, Mar 03 2024 *)
Formula
a(n) = permanent(m), where the n X n matrix m is defined by m(i,j) = 1 or 0 depending on whether i+j is a Fibonacci number or not.
Extensions
a(30)-a(50) from Ray Chandler, Jul 26 2004
More terms from David Wasserman, Dec 19 2007
a(0)=1 prepended by Stefano Spezia, Mar 04 2024
Comments