3,2

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

J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p, 99.

M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.

T. D. Noe, Table of n, a(n) for n=3..203

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.: x^3/((1-x)(1-2x)(1-4x)(1-8x)).

(With a different offset) a(n)=(-1+7*2^n-14*4^n+8*8^n)/21 - Jim Buddenhagen (jbuddenh(AT)gmail.com), Dec 14 2003

seq((-1+7*2^n-14*4^n+8*8^n)/21, n=1..20);

A006096:=1/(z-1)/(8*z-1)/(2*z-1)/(4*z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]

(Other) sage: [gaussian_binomial(n, 3, 2) for n in xrange(3, 23)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 24 2009]

Sequence in context: A017389 A157380 A098685 this_sequence A099915 A110557 A016304

Adjacent sequences: A006093 A006094 A006095 this_sequence A006097 A006098 A006099

nonn,easy,nice

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