0,1

a(n+3)=A^(n)B^(2)(1), n>=0, with compositions of Wythoff's complementary A(n):=A000201(n) and B(n)=A001950(n) sequences. See the W. Lang link under A135817 for the Wythoff representation of numbers (with A as 1 and B as 0 and the argument 1 omitted). E.g. 5=`00`, 8=`100`, 12=`1100`,..., in Wythoff code.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

D. Jarden, Recurring Sequences. Riveon Lematematika, Jerusalem, 1966.

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

G.f.: (3-4*x)/((1-x)*(1-x-x^2)). a(n)=a(n-1)+a(n-2)-1.

A001612:=-(-2+3*z**2)/(z-1)/(z**2+z-1); [Conjectured by S. Plouffe in his 1992 dissertation. Gives sequence except for the initial 3.]

(PARI) a(n)=fibonacci(n+1)+fibonacci(n-1)+1

Lucas sequence A000032 + 1.

Sequence in context: A039882 A164287 A086962 this_sequence A097092 A059320 A129601

Adjacent sequences: A001609 A001610 A001611 this_sequence A001613 A001614 A001615

nonn

N. J. A. Sloane (njas(AT)research.att.com).

Additional comments from Michael Somos, Jun 01 2000.