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%I #12 Sep 30 2021 11:42:23
%S 1,1,1,1,6,1,1,21,21,1,1,64,374,64,1,1,163,5900,5900,163,1,1,380,
%T 82587,644680,82587,380,1,1,809,1018388,66136870,66136870,1018388,809,
%U 1,1,1619,11174165,6057912073,52901629980,6057912073,11174165,1619,1,1,3049,110404788
%N 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 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 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 Álvar Ibeas, <a href="/A347975/b347975.txt">Entries up to T(10, 4)</a>
%H H. Fripertinger, <a href="http://www.mathe2.uni-bayreuth.de/frib/codes/tables.html">Isometry classes of codes</a>
%H Álvar Ibeas, <a href="/A347975/a347975.txt">Column k=1 up to n=100</a>
%H Álvar Ibeas, <a href="/A347975/a347975_1.txt">Column k=2 up to n=100</a>
%H Álvar Ibeas, <a href="/A347975/a347975_2.txt">Column k=3 up to n=100</a>
%H Álvar Ibeas, <a href="/A347975/a347975_3.txt">Column k=4 up to n=100</a>
%F T(n, 1) = T(n-1, 1) + A032193(n+8).
%e Triangle begins:
%e k: 0 1 2 3 4 5
%e --------------------------
%e n=0: 1
%e n=1: 1 1
%e n=2: 1 6 1
%e n=3: 1 21 21 1
%e n=4: 1 64 374 64 1
%e n=5: 1 163 5900 5900 163 1
%e 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 Cf. A022173, A032193, A241926.
%K nonn,tabl
%O 0,5
%A _Álvar Ibeas_, Sep 21 2021
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