This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(7) = 1 + 1 + 1 + 2 + 2 + 22 + 564 = 593 is prime.
a007283 = (* 3) . (2 ^) a007283_list = iterate (* 2) 3 -- Reinhard Zumkeller, Mar 18 2012, Feb 20 2012
[3*2^n: n in [0..30]]; // Vincenzo Librandi, May 18 2011
A007283:=n->3*2^n; seq(A007283(n), n=0..50); # Wesley Ivan Hurt, Dec 03 2013
Table[3(2^n), {n, 0, 32}] (* Alonso del Arte, Mar 24 2011 *)
A007283(n):=3*2^n$ makelist(A007283(n),n,0,30); /* Martin Ettl, Nov 11 2012 */
a(n)=3*2^n
a(n)=3<Charles R Greathouse IV, Oct 10 2012
def A007283(n): return 3<Chai Wah Wu, Feb 14 2023
(List.fill(40)(2: BigInt)).scanLeft(1: BigInt)( * ).map(3 * ) // _Alonso del Arte, Nov 28 2019
Table[Length[ResourceFunction["FindProperColorings"][GraphProduct[CompleteGraph[n], CompleteGraph[n], "Cartesian"], n]], {n, 5}]
a(3) = 1 because after 123 in the first row and column, 213 is not allowed for the second row, so it must be 231 and thus the third row is 312.
(* This script is not suitable for n > 6 *) matrices[n_ /; n > 1] := Module[{a, t, vars}, t = Table[Which[i==1, j, j==1, i, j>i, a[i, j], True, a[j, i]], {i, n}, {j, n}]; vars = Select[Flatten[t], !IntegerQ[#]& ] // Union; t /. {Reduce[And @@ (1 <= # <= n & /@ vars) && And @@ Unequal @@@ t, vars, Integers] // ToRules}]; a[0] = a[1] = 1; a[n_] := Length[ matrices[n]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 6}] (* Jean-François Alcover, Jan 04 2016 *)
For n=2, the only Latin squares of order 2 are [[1, 2], [2, 1]] and [[2, 1], [1, 2]]. Therefore, the minimum absolute value of the determinants of order 2 Latin squares is 3.
# Takes a string and turns it into a square matrix of order n
def make_matrix(string,n):
m = []
row = []
for i in range(0,n * n):
if string[i] == '\n':
continue
if string[i] == ' ':
continue
row.append(Integer(string[i]) + 1)
if len(row) == n:
m.append(row)
row = []
return matrix(m)
# Reads a file and returns a list of the matrices in the file
def fetch_matrices(file_name,n):
matrices = []
with open(file_name) as f:
L = f.readlines()
for i in L:
matrices.append(make_matrix(i,n))
return matrices
# Takes a matrix and permutates each symbol in the matrix
# with the given permutation
def permute_matrix(matrix, permutation,n):
copy = deepcopy(matrix)
for i in range(0, n):
for j in range(0 , n):
copy[i,j] = permutation[copy[i][j] - 1]
return copy
"""
Creates a determinant list with the following triples,
[Isotopy Class Representative, Permutation, Determinant]
The Isotopy class representatives come from a file that
contains all Isotopy classes.
"""
def create_determinant_list(file_name,n):
the_list = []
permu = (Permutations(n)).list()
matrices = fetch_matrices(file_name,n)
for i in range(0,len(matrices)):
for j in permu:
copy = permute_matrix(matrices[i],j,n)
the_list.append([i,j,copy.determinant()])
print(len(the_list))
return the_list
# Froylan Maldonado, Jun 28 2019
An example of an 8 X 8 Latin square with maximum determinant is [7 1 3 4 8 2 5 6] [1 7 4 3 6 5 2 8] [3 4 1 7 2 6 8 5] [4 3 7 1 5 8 6 2] [8 6 2 5 4 7 1 3] [2 5 6 8 7 3 4 1] [5 2 8 6 1 4 3 7] [6 8 5 2 3 1 7 4]. An example of a 9 X 9 Latin square with maximum determinant is [9 4 3 8 1 5 2 6 7] [3 9 8 5 4 6 1 7 2] [4 1 9 3 2 8 7 5 6] [1 2 4 9 7 3 6 8 5] [8 3 5 6 9 7 4 2 1] [2 7 1 4 6 9 5 3 8] [5 8 6 7 3 2 9 1 4] [7 6 2 1 5 4 8 9 3] [6 5 7 2 8 1 3 4 9]. An example of a 10 X 10 Latin square with abs(determinant) = 36843728625 is a circulant matrix with first row [1, 3, 7, 9, 8, 6, 5, 4, 2, 10], but it is not known if this is the best possible. - _Kebbaj Mohamed Reda_, Nov 27 2019 (reworded by _Hugo Pfoertner_)
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