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A015265
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Gaussian binomial coefficient [ n,2 ] for q = -13.
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12
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1, 157, 26690, 4508570, 761974851, 128773405047, 21762709934980, 3677897920745140, 621564749363392901, 105044442632566365137, 17752510805031727164870, 3000174326048697741925710, 507029461102251552321630151, 85687978926280231101185088427
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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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FORMULA
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G.f.: x^2/((1-x)*(1+13*x)*(1-169*x)). - Ralf Stephan, Apr 01 2004
a(2) = 1, a(3) = 157, a(4) = 26690, a(n) = 157*a(n-1) + 2041*a(n-2) - 2197*a(n-3). - Vincenzo Librandi, Oct 28 2012
a(n) = (1/2352)*( (1 - (-13)^n)*((-13)^(n-1) - 1) ). - M. F. Hasler, Nov 03 2012
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MATHEMATICA
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PROG
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(Sage) [gaussian_binomial(n, 2, -13) for n in range(2, 14)] # Zerinvary Lajos, May 27 2009
(Magma) I:=[1, 157, 26690]; [n le 3 select I[n] else 157*Self(n-1)+2041*Self(n-2)-2197*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Oct 28 2012
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CROSSREFS
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Cf. Gaussian binomial coefficients [n,2] for q=-2,...,-12: A015249, A015251, A015253, A015255, A015257 A015258, A015259, A015260, A015261, A015262, A015264.
Cf. Gaussian binomial coefficients [n,r] for q=-13: A015286 (r=3), 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
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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