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A015253
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Gaussian binomial coefficient [ n,2 ] for q=-4.
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4
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1, 13, 221, 3485, 55965, 894621, 14317213, 229062301, 3665049245, 58640578205, 938250090141, 15011998086813, 240191982810781, 3843071671285405, 61489146955314845, 983826350426044061, 15741221610252678813
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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.
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 2..200
Index entries for linear recurrences with constant coefficients, signature (13,52,-64).
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FORMULA
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G.f.: x^2/((1-x)*(1+4*x)*(1-16*x)).
a(2) = 1, a(3) = 13, a(4) = 221 a(n) = 13*(n-1) + 52*a(n-2) - 64*a(n-3). - _Vincenzo Librandi -, Oct 27 2012
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EXAMPLE
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G.f. = x^2 + 13*x^3 + 221*x^4 + 3485*x^5 + 55965*x^6 + 894621*x^7 + ...
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MATHEMATICA
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Rest[Table[QBinomial[n, 2, -4], {n, 20}]] (* Harvey P. Dale, Feb 26 2012 *)
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PROG
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(Sage) [gaussian_binomial(n, 2, -4) for n in xrange(2, 19)] # Zerinvary Lajos, May 27 2009
(MAGMA) I:=[1, 13, 221]; [n le 3 select I[n] else 13*Self(n-1) + 52*Self(n-2) - 64*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Oct 27 2012
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CROSSREFS
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Sequence in context: A218475 A059525 A086147 * A051621 A173427 A051180
Adjacent sequences: A015250 A015251 A015252 * A015254 A015255 A015256
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gérard
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STATUS
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approved
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