[math-fun] Comment re Allan Weshler's 1996 posting to the math-fun mailing list.
Sloane's ONline encyclopedia of integer sequences" lists Allan Weshler's J-Determinant sequence as sequence A022344. Until I rediscovered this sequence and added my own comments no information on this sequence was given except a reference to "Posting to math-fun mailing list dated December 4, 1996". Was this your mailing list? If so members may be interested in my following conjectures: Background: Every integer based Fibonacci sequence ultimately appears as a row, n, of Wtthoffs array (Sloane's sequence no A035513) and can be characterized by their J-Determinant as given by Allan Weshler's J-Determinant sequence (A022344 where a(n) = (the absolute value of F(n,i-1)*F(n,i+1) - F(n,i)^2, which is invariant with i varying. Also, in 1961 Horadam, Amer. Math. Monthly 68(1961) pp 751-753) showed that for any Fibonacci sequence, F, that the triple (2F(n+1)*F(n+2), F(n)*F(n+3),2F(n+1)*F(n+2) + F(n)^2) is a Pythagorean number triple (a,b,c) for all n, i.e. a^2 + b^2 = c^2. Conjecture 1: Let any two integer based Fibonacci sequences, F1 and F2, be sequences appearing in rows "n" and "m" respectively and thus have characteristic values, a(n) and a(m) respectively. Then there is a third Fibonacci sequence that is defined by F3(i) = F1(i)*F2(j+1) - F1(i+1)*F2(j) where j is a constant. This third Fibonacci sequence appears in a row, p, of Wythoffs array and has the characteristic value a(p) = a(n)*a(m). Conjecture 2: For every Fibonacci sequence having coprime adjacent terms and appearing in a row (n) of Wythoff's array, the "c" values of Horadam's Pythagorean triples, 2F(n+1)*F(n+2) -F(n)^2), where the c values are reduced by dividing through by the greatest common divisor, form the bijection of a Fibonacci sequence having the characteristic value of (a(n))^2. Anyone interested in this may refer to my further comments to sequences A035513, A022344 in Sloane's online encyclopedia and my own sequence (Sloane's A127561) which is a tabulation of terms, a(n) from A022344, as a table where the row and column positions dictate the starting values of a Fibonacci sequence having the characteristic value a(n), and which has very interesting prime modulus properties.
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