0,2

Also smaller of two consecutive integers whose cubes differ by a square. Defined by (a(n)+1)^3 - a(n)^3 = square.

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.

Problem E702, Amer. Math. Monthly, 53 (1946), 465.

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.

Sociedad Magic Penny Patagonia, Leonardo en Patagonia

a(n) = 15a(n-1) - 15a(n-2) + a(n-3).

a(n)=(s1*t1^n + s2*t2^n + 6)/12 where s1=3+2*sqrt(3), s2=3-2*sqrt(3), t1=7+4*sqrt(3), t2=7-4*sqrt(3).

A001922:=(-1+7*z)/(z-1)/(z**2-14*z+1); [Conjectured by S. Plouffe in his 1992 dissertation.]

Cf. A001921, A001570, A006051.

Let m be the n-th ratio 2/1, 7/4, 26/15, 97/56, 362/209, ... Then a(n)=m*(2-m)/(m^2-3). The numerators 2, 7, 26, ... of m are A001075. The denominators 1, 4, 15, ... of m are A001353.

a(n)=A001075(n)*A001353(n+1).

Sequence in context: A034300 A146346 A119934 this_sequence A113551 A082735 A024358

Adjacent sequences: A001919 A001920 A001921 this_sequence A001923 A001924 A001925

nonn,easy

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

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jul 04 2000

Additional comments from Jim Buddenhagen (jbuddenh(AT)gmail.com), Mar 04 2001