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A176233 Determinant of n X n matrix with rows (n^2,-1,0,...,0), (1,n^2,-1, 0,...,0), (0,1,n^2,-1,0,...,0), ...,(0,0,...,1,n^2). 3
1, 17, 747, 66305, 9828200, 2185188193, 679919101029, 281956264747009, 150277722869740455, 100090028003500150001, 81458362232421250207824, 79539026883848399173231873, 91771878445323959814042316673 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Each determinant is the numerator of the fraction x(n)/y(n) = [n^2, n^2, ..., n^2] (simple continued fraction). The value x(n) is obtained by computing the determinant det(n X n) along the last column. The value y(n) is obtained by computing this determinant after removal of the first row and the first column (see example below).
REFERENCES
J. M. De Koninck, A. Mercier, 1001 problèmes en théorie classique des nombres. Collection ellipses (2004), p. 115.
LINKS
FORMULA
a(n) ~ n^(2*n). - Vaclav Kotesovec, Dec 29 2019
EXAMPLE
For n = 1, det[1] = 1.
For n = 2, det(([[4,-1],[1,4]]) = 17, and the continued fraction expansion is 17/4 = [2^2,2^2].
For n = 3, det([[9,-1, 0],[1,9,-1],[0,1,9]])) = 747, and the continued fraction expansion is 747/det(([[9,-1],[1,9]]) = 747/82 = [3^2,3^2,3^2].
MAPLE
for n from 15 by -1 to 1 do x0:=n^2: for p from n by -1 to 2 do : x0:= n^2 + 1/x0 :od: print(x0): od :
MATHEMATICA
nmax = 20; Do[x0 = n^2; Do[x0 = n^2 + 1/x0, {p, n, 2, -1}]; a[n] = Numerator[x0]; , {n, nmax, 1, -1}]; Table[a[n], {n, 1, nmax}] (* Vaclav Kotesovec, Dec 29 2019 *)
CROSSREFS
Sequence in context: A171766 A283579 A294757 * A360647 A355495 A368492
KEYWORD
nonn
AUTHOR
Michel Lagneau, Apr 12 2010
STATUS
approved

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Last modified April 18 06:24 EDT 2024. Contains 371769 sequences. (Running on oeis4.)