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A015303
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Gaussian binomial coefficient [ n,4 ] for q = -13.
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12
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OFFSET
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4,2
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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 = 4..200
Index entries related to Gaussian binomial coefficients.
Index entries for linear recurrences with constant coefficients, signature (26521,58611410,-9905328290,-128011801489,137858491849).
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FORMULA
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a(n) = product_{i=1..4} ((-13)^(n-i+1)-1)/((-13)^i-1). - M. F. Hasler, Nov 03 2012
G.f.: -x^4 / ( (x-1)*(169*x-1)*(2197*x+1)*(13*x+1)*(28561*x-1) ). - R. J. Mathar, Aug 03 2016
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EXAMPLE
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To illustrate the relation qC(n,r)=qC(n,n-r), here with r=4, n=r+1...r+3:
A015303(5) = 26521 = A015000(5),
A015303(6) = 761974851 = A015265(6),
A015303(7) = 21752862899691 = A015286(7).
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MATHEMATICA
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Table[QBinomial[n, 4, -13], {n, 4, 20}] (* Vincenzo Librandi, Oct 29 2012 *)
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PROG
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(Sage) [gaussian_binomial(n, 4, -13) for n in range(4, 12)] # Zerinvary Lajos, May 27 2009
(PARI) A015303(n, r=4, q=-13)=prod(i=1, r, (q^(n-i+1)-1)/(q^i-1)) \\ M. F. Hasler, Nov 03 2012
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CROSSREFS
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Cf. q-integers and Gaussian binomial coefficients [n,r] for q=-13: A015000, A015265 (r=2), A015286 (r=3), 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
Fifth row (r=4) or column (resp. diagonal) of A015129, read as square (resp. triangular) array.
Sequence in context: A275417 A206539 A273260 * A236622 A329785 A229592
Adjacent sequences: A015300 A015301 A015302 * A015304 A015305 A015306
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gérard, Dec 11 1999
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STATUS
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approved
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