2,2

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=2..100

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/[(1-x)(1-3x)(1-9x)].

a(n) = (9^n - 4*3^n + 3)/48 - Mitch Harris (maharri(AT)gmail.com), Mar 23 2008

a:=n->sum((9^(n-j)-3^(n-j))/6, j=0..n): seq(a(n), n=1..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 15 2007

A006100:=-1/(z-1)/(3*z-1)/(9*z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]

(Other) sage: [gaussian_binomial(n, 2, 3) for n in xrange(2, 19)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 25 2009]

Sequence in context: A155623 A023061 A121033 this_sequence A037603 A037708 A142740

Adjacent sequences: A006097 A006098 A006099 this_sequence A006101 A006102 A006103

nonn

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