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A347975 Triangle read by rows: T(n, k) is the number of k-dimensional subspaces in (F_9)^n, counted up to coordinate permutation (n >= 0, 0 <= k <= n).

%I A347975 #12 Sep 30 2021 11:42:23
%S A347975 1,1,1,1,6,1,1,21,21,1,1,64,374,64,1,1,163,5900,5900,163,1,1,380,
%T A347975 82587,644680,82587,380,1,1,809,1018388,66136870,66136870,1018388,809,
%U A347975 1,1,1619,11174165,6057912073,52901629980,6057912073,11174165,1619,1,1,3049,110404788
%N A347975 Triangle read by rows: T(n, k) is the number of k-dimensional subspaces in (F_9)^n, counted up to coordinate permutation (n >= 0, 0 <= k <= n).
%C A347975 Columns can be computed by a method analogous to that of Fripertinger for isometry classes of linear codes, disallowing scalar transformation of individual coordinates.
%C A347975 Regarding the formula for column k = 1, note that A241926(q-1, n) counts, up to coordinate permutation, one-dimensional subspaces of (F_q)^n generated by a vector with no zero component.
%H A347975 Álvar Ibeas, <a href="/A347975/b347975.txt">Entries up to T(10, 4)</a>
%H A347975 H. Fripertinger, <a href="http://www.mathe2.uni-bayreuth.de/frib/codes/tables.html">Isometry classes of codes</a>
%H A347975 Álvar Ibeas, <a href="/A347975/a347975.txt">Column k=1 up to n=100</a>
%H A347975 Álvar Ibeas, <a href="/A347975/a347975_1.txt">Column k=2 up to n=100</a>
%H A347975 Álvar Ibeas, <a href="/A347975/a347975_2.txt">Column k=3 up to n=100</a>
%H A347975 Álvar Ibeas, <a href="/A347975/a347975_3.txt">Column k=4 up to n=100</a>
%F A347975 T(n, 1) = T(n-1, 1) + A032193(n+8).
%e A347975 Triangle begins:
%e A347975   k:  0    1    2    3    4    5
%e A347975       --------------------------
%e A347975 n=0:  1
%e A347975 n=1:  1    1
%e A347975 n=2:  1    6    1
%e A347975 n=3:  1   21   21    1
%e A347975 n=4:  1   64  374   64    1
%e A347975 n=5:  1  163 5900 5900  163    1
%e A347975 There are 10 = A022173(2, 1) one-dimensional subspaces in (F_9)^2. Among them, <(1, 1)> and <(1, 2)> are invariant by coordinate swap and the rest are grouped in orbits of size two. Hence, T(2, 1) = 6.
%Y A347975 Cf. A022173, A032193, A241926.
%K A347975 nonn,tabl
%O A347975 0,5
%A A347975 _Álvar Ibeas_, Sep 21 2021