A347974 - OEIS

%I #8 Sep 30 2021 11:42:27

%S 1,1,1,1,5,1,1,17,17,1,1,47,242,47,1,1,113,3071,3071,113,1,1,245,

%T 34477,232290,34477,245,1,1,491,341633,16665755,16665755,341633,491,1,

%U 1,920,3022045,1073874283,8241549097,1073874283,3022045,920,1,1,1635,24145695

%N 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 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="/A347974/b347974.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="/A347974/a347974.txt">Column k=1 up to n=100</a>

%H Álvar Ibeas, <a href="/A347974/a347974_1.txt">Column k=2 up to n=100</a>

%H Álvar Ibeas, <a href="/A347974/a347974_2.txt">Column k=3 up to n=100</a>

%H Álvar Ibeas, <a href="/A347974/a347974_3.txt">Column k=4 up to n=100</a>

%F T(n, 1) = T(n - 1, 1) + A032192(n + 7).

%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    5    1

%e n=3:  1   17   17    1

%e n=4:  1   47  242   47    1

%e n=5:  1  113 3071 3071  113    1

%e 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 Cf. A022172, A032192, A241926.

%K nonn,tabl

%O 0,5

%A _Álvar Ibeas_, Sep 21 2021