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A006121
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Sum of Gaussian binomial coefficients [ n,k ] for q=7.
(Formerly M1984)
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4
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1, 2, 10, 116, 3652, 285704, 61946920, 33736398032, 51083363186704, 194585754101247008, 2061787082699360148640, 54969782721182164414355264
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OFFSET
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0,2
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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.
Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.
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LINKS
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Table of n, a(n) for n=0..11.
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FORMULA
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a(n) = 2*a(n-1)+(7^(n-1)-1)*a(n-2), (Goldman + Rota, 1969). - Vaclav Kotesovec, Aug 21 2013
a(n) ~ c * 7^(n^2/4), where c = EllipticTheta[3,0,1/7]/QPochhammer[1/7,1/7] = 1.537469386940... if n is even and c = EllipticTheta[2,0,1/7]/QPochhammer[1/7,1/7] = 1.499386995418... if n is odd. - Vaclav Kotesovec, Aug 21 2013
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MATHEMATICA
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Flatten[{1, RecurrenceTable[{a[n]==2*a[n-1]+(7^(n-1)-1)*a[n-2], a[0]==1, a[1]==2}, a, {n, 1, 15}]}] (* Vaclav Kotesovec, Aug 21 2013 *)
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CROSSREFS
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Sequence in context: A187653 A131811 A261496 * A110951 A172477 A120597
Adjacent sequences: A006118 A006119 A006120 * A006122 A006123 A006124
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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