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 A006119 Sum of Gaussian binomial coefficients [ n,k ] for q=5. (Formerly M1898) 6
 1, 2, 8, 64, 1120, 42176, 3583232, 666124288, 281268665344, 260766671206400, 549874114073747456, 2547649010961476288512, 26854416724405008878829568 (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..75 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)+(5^(n-1)-1)*a(n-2), (Goldman + Rota, 1969). - Vaclav Kotesovec, Aug 21 2013 a(n) ~ c * 5^(n^2/4), where c = EllipticTheta[3,0,1/5]/QPochhammer[1/5,1/5] = 1.845509008203... if n is even and c = EllipticTheta[2,0,1/5]/QPochhammer[1/5,1/5] = 1.829548121746... if n is odd. - Vaclav Kotesovec, Aug 21 2013 MATHEMATICA Flatten[{1, RecurrenceTable[{a[n]==2*a[n-1]+(5^(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, 5], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Aug 13 2016 *) PROG MAGMA) [n le 2 select n else 2*Self(n-1)+(5^(n-2)-1)*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Aug 13 2016 CROSSREFS Row sums of triangle A022169. Sequence in context: A139685 A006125 A193753 * A296328 A322066 A255133 Adjacent sequences:  A006116 A006117 A006118 * A006120 A006121 A006122 KEYWORD nonn AUTHOR STATUS approved

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Last modified April 18 16:51 EDT 2021. Contains 343089 sequences. (Running on oeis4.)