cp's OEIS Frontend

A347974 Triangle read by rows: T(n, k) is the number of k-dimensional subspaces in (F_8)^n, counted up to coordinate permutation (n >= 0, 0 <= k <= n).

%I A347974 #8 Sep 30 2021 11:42:27
%S A347974 1,1,1,1,5,1,1,17,17,1,1,47,242,47,1,1,113,3071,3071,113,1,1,245,
%T A347974 34477,232290,34477,245,1,1,491,341633,16665755,16665755,341633,491,1,
%U A347974 1,920,3022045,1073874283,8241549097,1073874283,3022045,920,1,1,1635,24145695
%N A347974 Triangle read by rows: T(n, k) is the number of k-dimensional subspaces in (F_8)^n, counted up to coordinate permutation (n >= 0, 0 <= k <= n).
%C A347974 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 A347974 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 A347974 Álvar Ibeas, <a href="/A347974/b347974.txt">Entries up to T(10, 4)</a>
%H A347974 H. Fripertinger, <a href="http://www.mathe2.uni-bayreuth.de/frib/codes/tables.html">Isometry classes of codes</a>
%H A347974 Álvar Ibeas, <a href="/A347974/a347974.txt">Column k=1 up to n=100</a>
%H A347974 Álvar Ibeas, <a href="/A347974/a347974_1.txt">Column k=2 up to n=100</a>
%H A347974 Álvar Ibeas, <a href="/A347974/a347974_2.txt">Column k=3 up to n=100</a>
%H A347974 Álvar Ibeas, <a href="/A347974/a347974_3.txt">Column k=4 up to n=100</a>
%F A347974 T(n, 1) = T(n - 1, 1) + A032192(n + 7).
%e A347974 Triangle begins:
%e A347974   k:  0    1    2    3    4    5
%e A347974       --------------------------
%e A347974 n=0:  1
%e A347974 n=1:  1    1
%e A347974 n=2:  1    5    1
%e A347974 n=3:  1   17   17    1
%e A347974 n=4:  1   47  242   47    1
%e A347974 n=5:  1  113 3071 3071  113    1
%e A347974 There are 9 = A022172(2, 1) one-dimensional subspaces in (F_8)^2. Among them, <(1, 1)> is invariant by coordinate swap and the rest are grouped in orbits of size two. Hence, T(2, 1) = 5.
%Y A347974 Cf. A022172, A032192, A241926.
%K A347974 nonn,tabl
%O A347974 0,5
%A A347974 _Álvar Ibeas_, Sep 21 2021