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A006111
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Gaussian binomial coefficient [ n,2 ] for q=5.
(Formerly M5228)
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1
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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; internal format)
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OFFSET
| 2,2
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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.
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LINKS
| 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.
Index to sequences with linear recurrences with constant coefficients, signature (31,-155,125)
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FORMULA
| G.f.: x^2/[(1-x)(1-5x)(1-25x)].
a(n) = 6*a(n-1) -5*a(n-2) +25^(n-2), n>=4. - Vincenzo Librandi, Mar 20 2011
a(n) = 30*a(n-1) -125*a(n-2) +1, n>=3. - Vincenzo Librandi, Mar 20 2011
a(n) = -5^(n-1)/16 +25^n/480 +1/96 . - R. J. Mathar, Mar 21 20111
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MAPLE
| A006111:=-1/(z-1)/(25*z-1)/(5*z-1); [S. Plouffe in his 1992 dissertation with offset 0.]
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MATHEMATICA
| Transpose[NestList[Flatten[{Last[#], 30Last[#]- 125First[#]+1}]&, {1, 31}, 20]] [[1]] (* From 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
| (Other) sage: [gaussian_binomial(n, 2, 5) for n in xrange(2, 16)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
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CROSSREFS
| Sequence in context: A166488 A051587 A069380 * A183828 A180847 A202977
Adjacent sequences: A006108 A006109 A006110 * A006112 A006113 A006114
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Harvey P. Dale, Mar 26 2011.
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