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 A006118 Sum of Gaussian binomial coefficients [ n,k ] for q=4. (Formerly M1812) 8
 1, 2, 7, 44, 529, 12278, 565723, 51409856, 9371059621, 3387887032202, 2463333456292207, 3557380311703796564, 10339081666350180289849, 59703612489554311631068958 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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. 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. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..80 S. Hitzemann, W. Hochstattler, On the combinatorics of Galois numbers, Discr. Math. 310 (2010) 3551-3557. Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1. M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351. (Annotated scanned copy) FORMULA a(n) = 2*a(n-1)+(4^(n-1)-1)*a(n-2), n>1. [Hitzemann and Hochstattler]. - R. J. Mathar, Aug 21 2013 a(n) ~ c * 4^(n^2/4), where c = EllipticTheta[3,0,1/4]/QPochhammer[1/4,1/4] = 2.189888057761... if n is even and c = EllipticTheta[2,0,1/4]/QPochhammer[1/4,1/4] = 2.182810929357... if n is odd. - Vaclav Kotesovec, Aug 21 2013 MATHEMATICA Flatten[{1, RecurrenceTable[{a[n]==2*a[n-1]+(4^(n-1)-1)*a[n-2], a[0]==1, a[1]==2}, a, {n, 1, 15}]}] (* Vaclav Kotesovec, Aug 21 2013 *) Table[Sum[QBinomial[n, k, 4], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Aug 13 2016 *) PROG (Magma) [n le 2 select n else 2*Self(n-1)+(4^(n-2)-1)*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Aug 13 2016 CROSSREFS Row sums of triangle A022168. Sequence in context: A278295 A356613 A107354 * A083670 A270357 A367787 Adjacent sequences: A006115 A006116 A006117 * A006119 A006120 A006121 KEYWORD nonn AUTHOR N. J. A. Sloane STATUS approved

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Last modified June 24 15:31 EDT 2024. Contains 373679 sequences. (Running on oeis4.)