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 A006105 Gaussian binomial coefficient [ n,2 ] for q=4. (Formerly M5115) 10
 1, 21, 357, 5797, 93093, 1490853, 23859109, 381767589, 6108368805, 97734250405, 1563749404581, 25019996065701, 400319959420837, 6405119440211877, 102481911401303973 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 REFERENCES 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. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351. LINKS Vincenzo Librandi, Table of n, a(n) for n = 2..200 Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992. M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351. (Annotated scanned copy) Index entries for linear recurrences with constant coefficients, signature (21,-84,64) FORMULA G.f.: x^2/((1-x)*(1-4*x)*(1-16*x)). [Multiplied by x^2 to match offset by R. J. Mathar, Mar 11 2009] a(n) = (16^n - 5*4^n + 4)/180. - Mitch Harris, Mar 23 2008 a(n) = 5*a(n-1) -4*a(n-2) +16^(n-2), n>=4. - Vincenzo Librandi, Mar 20 2011 MAPLE A006105:=-1/(z-1)/(4*z-1)/(16*z-1); # Simon Plouffe in his 1992 dissertation, assuming offset zero MATHEMATICA faq[n_, q_] = Product[(1-q^(1+k))/(1-q), {k, 0, n-1}]; qbin[n_, m_, q_] = faq[n, q]/(faq[m, q]*faq[n-m, q]); Table[qbin[n, 2, 4], {n, 2, 16}] (* Jean-François Alcover, Jul 21 2011 *) CoefficientList[Series[1 / ((1 - x) (1 - 4 x) (1 - 16 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 23 2013 *) PROG (Sage) [gaussian_binomial(n, 2, 4) for n in xrange(2, 17)] # Zerinvary Lajos, May 28 2009 CROSSREFS Sequence in context: A271633 A184289 A192093 * A167032 A051564 A302308 Adjacent sequences:  A006102 A006103 A006104 * A006106 A006107 A006108 KEYWORD nonn AUTHOR STATUS approved

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Last modified March 24 19:59 EDT 2019. Contains 321448 sequences. (Running on oeis4.)