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A006111
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Gaussian binomial coefficient [ n,2 ] for q=5.
(Formerly M5228)
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2
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1, 31, 806, 20306, 508431, 12714681, 317886556, 7947261556, 198682027181, 4967053120931, 124176340230306, 3104408566792806, 77610214474995931, 1940255363400777181, 48506384092648824056, 1212659602354367574056, 30316490059049924214681
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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2,2
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REFERENCES
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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.
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LINKS
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FORMULA
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G.f.: x^2/[(1-x)(1-5x)(1-25x)].
a(n) = -5^(n-1)/16 + 25^n/480 + 1/96. - R. J. Mathar, Mar 21 2011
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MAPLE
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MATHEMATICA
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Transpose[NestList[Flatten[{Last[#], 30Last[#]- 125First[#]+1}]&, {1, 31}, 20]] [[1]] (* Harvey P. Dale, Mar 26 2011 *)
LinearRecurrence[{31, -155, 125}, {1, 31, 806}, 10] (* T. D. Noe, Mar 26 2011 *)
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PROG
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(Sage) [gaussian_binomial(n, 2, 5) for n in range(2, 16)] # Zerinvary Lajos, May 28 2009
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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