0,2

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).

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.

A. Brousseau, A sequence of power formulas, Fib. Quart., 6 (1968), 81-83.

A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 74.

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.: (1 + x - x^2 )^-1 (1 - 4x - x^2 )^-1.

G.f.: 1/(1-3*x-6*x^2+3*x^3+x^4) = 1/((1+x-x^2)*(1-4*x-x^2)) (see Comments to A055870). a(n)=A010048(n+3, 3)= fibonomial(n+3, 3). Recursion: a(n)= 4*a(n-1)+a(n-2)+((-1)^n)*F(n+1), n >= 2; a(0)=1, a(1)=3.

A001655:=1/(z**2-z-1)/(z**2+4*z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]

Table[(Fibonacci[n+2]*Fibonacci[n+1]*Fibonacci[n])/2, {n, 0, 40}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 23 2009]

Equals 1/2 * A065563(n).

First differences are in A066258.

Sequence in context: A036750 A058748 A049314 this_sequence A128237 A058749 A072336

Adjacent sequences: A001652 A001653 A001654 this_sequence A001656 A001657 A001658

nonn,easy,new

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