A060868
Number of n X n matrices over GF(3) with rank 1.
Original entry on oeis.org
2, 32, 338, 3200, 29282, 264992, 2389298, 21516800, 193690562, 1743333152, 15690352658, 141214236800, 1270931319842, 11438391444512, 102945551698418, 926510051379200, 8338590720693122, 75047317261079072, 675425857674234578, 6078832726041680000, 54709494555295826402
Offset: 1
Ahmed Fares (ahmedfares(AT)my-deja.com), May 04 2001
a(2) = 32 because there are 33 (the second element in sequence A060705) singular 2 X 2 matrices over GF(3), that have rank <= 1 of which only the zero matrix has rank zero so a(2) = 33 - 1 = 32.
A379587
Array read by ascending antidiagonals: A(n, k) = (k^n - 1)^2/(k - 1), with k >= 2.
Original entry on oeis.org
0, 1, 0, 9, 2, 0, 49, 32, 3, 0, 225, 338, 75, 4, 0, 961, 3200, 1323, 144, 5, 0, 3969, 29282, 21675, 3844, 245, 6, 0, 16129, 264992, 348843, 97344, 9245, 384, 7, 0, 65025, 2389298, 5589675, 2439844, 335405, 19494, 567, 8, 0, 261121, 21516800, 89467563, 61027344, 12090125, 960000, 37303, 800, 9, 0
Offset: 0
The array begins as:
0, 0, 0, 0, 0, 0, ...
1, 2, 3, 4, 5, 6, ...
9, 32, 75, 144, 245, 384, ...
49, 338, 1323, 3844, 9245, 19494, ...
225, 3200, 21675, 97344, 335405, 960000, ...
961, 29282, 348843, 2439844, 12090125, 47073606, ...
...
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A[n_,k_]:=(k^n-1)^2/(k-1); Table[A[n-k+2,k],{n,0,9},{k,2,n+2}]//Flatten
A085404
Number of n X n matrices over GF(4) with rank n-1.
Original entry on oeis.org
1, 75, 79380, 1310904000, 344319762124800, 1444887697908695040000, 96976611786040182520676352000, 104131021972308383324202529613414400000, 1788970984376098024967914354100894418012733440000
Offset: 1
Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 31 2003
A345963
a(n) = (q^2-q+1)/3 where q = 2^(2*n+1) = A004171(n).
Original entry on oeis.org
1, 19, 331, 5419, 87211, 1397419, 22366891, 357903019, 5726579371, 91625794219, 1466014804651, 23456245263019, 375299957762731, 6004799458421419, 96076791871613611, 1537228672093301419, 24595658762082757291, 393530540227683855019, 6296488643780380633771, 100743818301035845954219
Offset: 0
-
a:= n-> (q-> (q^2-q+1)/3)(2^(2*n+1)):
seq(a(n), n=0..20); # Alois P. Heinz, Jun 30 2021
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Table[(2^(4*n + 2) - 2^(2*n + 1) + 1)/3, {n, 0, 19}] (* Amiram Eldar, Jun 30 2021 *)
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a(n) = my(q=2^(2*n+1)); (q^2-q+1)/3;
Showing 1-4 of 4 results.