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 A015286 Gaussian binomial coefficient [ n,3 ] for q = -13. 12
 1, -2040, 4508570, -9900819720, 21752862899691, -47790911017216080, 104996653267533662740, -230677643550873536294640, 506798783502833908602716981, -1113436927250681654567602842120 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 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 = 3..200 Index entries for linear recurrences with constant coefficients, signature (-2040,346970,4481880,-4826809) FORMULA a(n) = Product_{i=1..3} ((-13)^(n-i+1) - 1)/((-13)^i - 1). - M. F. Hasler, Nov 03 2012 G.f.: x^3 / ( (x-1)*(2197*x+1)*(13*x+1)*(169*x-1) ). - R. J. Mathar, Aug 03 2016 EXAMPLE A015286(7) = 21752862899691 = A015303(7), A015286(8) = -47790911017216080 = A015321(8), A015286(9) = 104996653267533662740 = A015337(9). - M. F. Hasler, Nov 03 2012 MATHEMATICA QBinomial[Range[3, 15], 3, -13] (* Harvey P. Dale, Jun 21 2012 *) Table[QBinomial[n, 3, -13], {n, 3, 20}] (* Vincenzo Librandi, Oct 28 2012 *) PROG (Sage) [gaussian_binomial(n, 3, -13) for n in range(3, 13)] # Zerinvary Lajos, May 27 2009 (PARI) A015286(n, r=3, q=-13)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012 (MAGMA) r:=3; q:=-13; [&*[(1-q^(n-i+1))/(1-q^i): i in [1..r]]: n in [r..20]]; // Vincenzo Librandi, Aug 02 2016 CROSSREFS Cf. Gaussian binomial coefficients [n,r] for q=-13: A015265 (r=2), A015303 (r=4), A015321 (r=5), A015337 (r=6), A015355 (r=7), A015370 (r=8), A015385 (r=9), A015402 (r=10), A015422 (r=11), A015438 (r=12). - M. F. Hasler, Nov 03 2012 Fourth row (r=3) or column (resp. diagonal) in A015129 (read as square array resp. triangle). - M. F. Hasler, Nov 03 2012 Sequence in context: A258965 A250009 A015158 * A172594 A115553 A068264 Adjacent sequences:  A015283 A015284 A015285 * A015287 A015288 A015289 KEYWORD sign,easy AUTHOR Olivier Gérard, Dec 11 1999 STATUS approved

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Last modified January 22 10:52 EST 2020. Contains 331144 sequences. (Running on oeis4.)