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 A303260 Determinant of n X n matrix A[i,j] = (j - i - 1 mod n) + [i=j], i.e., the circulant having (n, 0, 1, ..., n-2) as first row. 5
 1, 1, 4, 28, 273, 3421, 52288, 941578, 19505545, 456790123, 11931215316, 343871642632, 10840081272265, 371026432467913, 13702802011918048, 543154131059225686, 23000016472483168305, 1036227971225610466711, 49492629462587441963140, 2497992686980609418282548, 132849300060919364474261281 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS It is remarkable that for odd n, this determinant has its base n+1 digits equal to the middle row: e.g., a(9) = 456790123 is the determinant of the circulant matrix having [4,5,6,7,9,0,1,2,3] as middle row. a(0) = 1 is (by convention) the determinant of a 0 X 0 matrix. LINKS Table of n, a(n) for n=0..20. Max Alekseyev, Illustration for a(9) = 456790123 = A219324(20). N. I. Belukhov, Solution to Problem 14.7 (in Russian), Matematicheskoe Prosveshchenie 15 (2011), pp. 241-244. Wikipedia, Circulant matrix. FORMULA a(n) = det(I(n) + C(n)), where I(n) is the n X n identity matrix and C(n) is the circulant having (n-1, ..., 0) as first column. EXAMPLE a(5) = 3421 is the determinant of the matrix ( 5 0 1 2 3 ) ( 3 5 0 1 2 ) ( 2 3 5 0 1 ) and 3421 = 23501[6], i.e., written in base 6. ( 1 2 3 5 0 ) ( 0 1 2 3 5 ). PROG (PARI) a(n)=matdet(matrix(n, n, i, j, (j-i-1)%n+(i==j))) (Python) from sympy import Matrix def A303260(n): return Matrix(n, n, lambda i, j:(j-i-1) % n + (i==j)).det() # Chai Wah Wu, Oct 18 2021 CROSSREFS Cf. A081131(n+1) = determinant of the circulant matrix C(n) defined in formula, A070896 (signed variant). See also A219324. Sequence in context: A081917 A302583 A302605 * A174494 A128318 A032274 Adjacent sequences: A303257 A303258 A303259 * A303261 A303262 A303263 KEYWORD nonn AUTHOR M. F. Hasler, Apr 23 2018 STATUS approved

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Last modified September 24 17:02 EDT 2023. Contains 365579 sequences. (Running on oeis4.)