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 A015258 Gaussian binomial coefficient [ n,2 ] for q = -7. 3
 1, 43, 2150, 105050, 5149551, 252313293, 12363454300, 605808540100, 29684623509101, 1454546516636543, 71272779562356450, 3492366196825305150, 171125943656551078651, 8385171239086224969793, 410873390715818468708600, 20132796145070950850400200 (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. M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351. LINKS Vincenzo Librandi, Table of n, a(n) for n = 2..200 Index entries for linear recurrences with constant coefficients, signature (43,301,-343). FORMULA G.f.: x^2/((1-x)*(1+7x)*(1-49x)). a(n) = (6*(-7)^n - 7 +49^n)/2688. - R. J. Mathar, May 25 2011 a(n) = 43*a(n-1) + 301*a(n-2) - 343*a(n-3), n >= 5. - Harvey P. Dale, May 25 2011 MATHEMATICA CoefficientList[Series[1/((1-x)(1+7x)(1-49x)), {x, 0, 20}], x] (* or *) LinearRecurrence[{43, 301, -343}, {1, 43, 2150}, 20] (* Harvey P. Dale, May 25 2011 *) Table[QBinomial[n, 2, -7], {n, 2, 20}] (* Vincenzo Librandi, Oct 27 2012 *) PROG (Sage) [gaussian_binomial(n, 2, -7) for n in range(2, 16)] # Zerinvary Lajos, May 27 2009 (MAGMA) I:=[1, 43, 2150]; [n le 3 select I[n] else 43*Self(n-1) + 301*Self(n-2) - 343*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 27 2012 CROSSREFS Sequence in context: A267532 A335207 A076572 * A130014 A246535 A265234 Adjacent sequences:  A015255 A015256 A015257 * A015259 A015260 A015261 KEYWORD nonn,easy AUTHOR Olivier Gérard, Dec 11 1999 STATUS approved

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Last modified June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)