A015212 - OEIS

%I #19 May 14 2019 17:57:20

%S 1,2,24,928,224096,180925632,915592324864,15519120649837568,

%T 1649093881865807133696,586980815917441872922703872,

%U 1309843539264798142345101012967424,9790772765676733007363874643686313525248

%N Sum of Gaussian binomial coefficients for q=21.

%D 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.

%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.

%D M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.

%H Vincenzo Librandi, <a href="/A015212/b015212.txt">Table of n, a(n) for n = 0..50</a>

%H Kent E. Morrison, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL9/Morrison/morrison37.html">Integer Sequences and Matrices Over Finite Fields</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

%F a(0) = 1, a(1) = 2, a(n) = 2*a(n-1) + a(n-2)*((21^(n-1)) - 1). - _Vincenzo Librandi_, Nov 02 2012

%t Total/@Table[QBinomial[n, m, 21], {n, 0, 20}, {m, 0, n}] (* _Vincenzo Librandi_, Nov 02 2012 *)

%Y Row sums of triangle A022185.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, _Olivier Gérard_