cp's OEIS Frontend

A347973 Triangle read by rows: T(n, k) is the number of k-dimensional subspaces in (F_7)^n, counted up to coordinate permutation (n >= 0, 0 <= k <= n).

%I A347973 #8 Sep 30 2021 11:42:19
%S A347973 1,1,1,1,5,1,1,15,15,1,1,37,162,37,1,1,79,1538,1538,79,1,1,159,13237,
%T A347973 74830,13237,159,1,1,291,102019,3546909,3546909,102019,291,1,1,508,
%U A347973 708712,153181682,1010416196,153181682,708712,508,1,1,843,4473998,5954653026,267444866627
%N A347973 Triangle read by rows: T(n, k) is the number of k-dimensional subspaces in (F_7)^n, counted up to coordinate permutation (n >= 0, 0 <= k <= n).
%C A347973 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 A347973 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 A347973 Álvar Ibeas, <a href="/A347973/b347973.txt">Entries up to T(10, 4)</a>
%H A347973 H. Fripertinger, <a href="http://www.mathe2.uni-bayreuth.de/frib/codes/tables.html">Isometry classes of codes</a>
%H A347973 Álvar Ibeas, <a href="/A347973/a347973.txt">Column k=1 up to n=100</a>
%H A347973 Álvar Ibeas, <a href="/A347973/a347973_1.txt">Column k=2 up to n=100</a>
%H A347973 Álvar Ibeas, <a href="/A347973/a347973_2.txt">Column k=3 up to n=100</a>
%H A347973 Álvar Ibeas, <a href="/A347973/a347973_3.txt">Column k=4 up to n=100</a>
%F A347973 T(n, 1) = T(n - 1, 1) + A032191(n + 6).
%e A347973 Triangle begins:
%e A347973   k:  0    1    2    3    4    5
%e A347973       --------------------------
%e A347973 n=0:  1
%e A347973 n=1:  1    1
%e A347973 n=2:  1    5    1
%e A347973 n=3:  1   15   15    1
%e A347973 n=4:  1   37  162   37    1
%e A347973 n=5:  1   79 1538 1538   79    1
%e A347973 There are 8 = A022171(2, 1) one-dimensional subspaces in (F_7)^2. Two of them (<(1, 1)> and <(1, 6)>) are invariant by coordinate swap, while the rest are grouped in orbits of size two. Hence, T(2, 1) = 5.
%Y A347973 Cf. A022171, A032191, A241926.
%K A347973 nonn,tabl
%O A347973 0,5
%A A347973 _Álvar Ibeas_, Sep 21 2021