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 A015253 Gaussian binomial coefficient [ n,2 ] for q = -4. 4
 1, 13, 221, 3485, 55965, 894621, 14317213, 229062301, 3665049245, 58640578205, 938250090141, 15011998086813, 240191982810781, 3843071671285405, 61489146955314845, 983826350426044061, 15741221610252678813 (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 (13,52,-64). FORMULA 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 EXAMPLE G.f. = x^2 + 13*x^3 + 221*x^4 + 3485*x^5 + 55965*x^6 + 894621*x^7 + ... MATHEMATICA Rest[Table[QBinomial[n, 2, -4], {n, 20}]] (* Harvey P. Dale, Feb 26 2012 *) PROG (Sage) [gaussian_binomial(n, 2, -4) for n in range(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 CROSSREFS Sequence in context: A059525 A086147 A329073 * A051621 A173427 A051180 Adjacent sequences:  A015250 A015251 A015252 * A015254 A015255 A015256 KEYWORD nonn,easy AUTHOR Olivier Gérard, Dec 11 1999 STATUS approved

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Last modified September 23 09:53 EDT 2021. Contains 347612 sequences. (Running on oeis4.)