OFFSET
1,2
FORMULA
Conjectures from Colin Barker, May 22 2016: (Start)
a(n) = (-11+(-1)^n+2^(-1/2+(3*n)/2)*(3-3*(-1)^n+5*sqrt(2)+5*(-1)^n*sqrt(2)))/14.
a(n) = 5*(2^(3*n/2)-1)/7 for n even.
a(n) = 3*(2^((3*n)/2-1/2)-2)/7 for n odd.
a(n) = 9*a(n-2)-8*a(n-4) for n>4.
G.f.: x^2*(5+6*x) / ((1-x)*(1+x)*(1-8*x^2)).
(End)
MATHEMATICA
ok[n_] := Block[{x = IntegerDigits[n, 2]}, x == BitXor @@@ Transpose@ {RotateLeft@ x, RotateRight@ x}]; Select[ Range[0, 10^5], ok] (* Giovanni Resta, May 14 2016 *)
ok[n_] := Block[{x = IntegerDigits[n, 2]}, x == BitXor @@@ Transpose[ {RotateLeft[x], RotateRight[x]}]]; Select[LinearRecurrence[{0, 9, 0, -8}, {0, 5, 6, 45}, 100], ok] (* Jean-François Alcover, May 22 2016, after Giovanni Resta *)
PROG
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Alex Ratushnyak, May 13 2016
EXTENSIONS
a(19)-a(27) from Giovanni Resta, May 14 2016
STATUS
approved