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.

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^2/[(1-x)(1-4x)(1-16x)].

(16^n - 5*4^n + 4)/180 - Mitch Harris (maharri(AT)gmail.com), Mar 23 2008

A006105:=-1/(z-1)/(4*z-1)/(16*z-1); [S. Plouffe in his 1992 dissertation, assuming offset zero.]

(Other) sage: [gaussian_binomial(n, 2, 4) for n in xrange(2, 17)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]

Sequence in context: A068705 A144864 A075921 this_sequence A167032 A051564 A108495

Adjacent sequences: A006102 A006103 A006104 this_sequence A006106 A006107 A006108

nonn

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

Removed attribute "conjectured" from Plouffe g.f. Multiplied g.f. by x^2 to match offset R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 11 2009