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%I #22 Mar 05 2024 09:07:35
%S 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,
%T 288,48,64,2304,1600,10800,288,432,8,675,650,1,26,9,10400,1600,576,
%U 2304,23040,576,2560,1024,368640,516096,128000,2240000,5832000,32256,2304,46656,64,96,91125,3750,84500,6,1,676,9,261
%N Number of permutations p of (1,2,3,...,n) such that k+p(k) is a Fibonacci number for 1 <= k <= n.
%C See A097083 for the positive values of n such that a(n) = 1.
%F 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.
%t 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 *)
%Y Cf. A010056, A073364, A095986, A097083.
%K nonn
%O 0,5
%A _John W. Layman_, Jul 23 2004
%E a(30)-a(50) from _Ray Chandler_, Jul 26 2004
%E More terms from _David Wasserman_, Dec 19 2007
%E a(0)=1 prepended by _Stefano Spezia_, Mar 04 2024
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