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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 Table of n, a(n) for n=1..13. 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 Cf. A001040, A036245, A036246, A084845, A176232. Sequence in context: A171766 A283579 A294757 * A360647 A355495 A368492 Adjacent sequences: A176230 A176231 A176232 * A176234 A176235 A176236 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.)