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 A286012 A Kedlaya-Wilf matrix for the Fibonacci sequence A000045. 0
 1, 1, 1, 1, 2, 2, 1, 3, 6, 3, 1, 4, 12, 17, 5, 1, 5, 20, 48, 50, 8, 1, 6, 30, 102, 197, 147, 13, 1, 7, 42, 185, 532, 815, 434, 21, 1, 8, 56, 303, 1165, 2804, 3391, 1282, 34 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS For any power series f(x) starting with the term x the first column of the Kedlaya-Wilf matrix are the coefficients of f(x), the second column are the coefficients of f(f(x)), the third column are the coefficients of f(f(f(x))) and so on. This gives a matrix with first row consisting of ones. The sequence given is the diagonal reading of this matrix from right up to left down. LINKS Table of n, a(n) for n=1..45. Kiran S. Kedlaya, Another Combinatorial Determinant, Journal of Combinatorial Theory Series A 90(1), November 1998. FORMULA As an n X n matrix a(i,j) = coefficient of x^i in f^(j)(x) for i,j=1..n where f^(j) is the j-fold composition of f with itself. EXAMPLE f^(3)(x) = x + 3x^2 + 12x^4 + ... as in A283679, so a(4)=1, a(8)=3, a(13)=12. MAPLE h:= x-> x/(1-x-x^2): h2:= n-> coeff(series(h(h(x))), x, n+1), x, n): h3:= n -> coeff(series(h(h2(x))), x, n+1), x, n): etc. h7:= n -> coeff(series(h(h6(x))), x, n+1), x, n): N7:=array(1..7, 1..7, sparse): gg:=array([h1, h2, h3, h4, h5, h6, h7]):for k from 1 to 7 do: for j from 1 to 7 do: N7[k, j]:=coeff(series(gg[j], x, 12), x^k): od:od: CROSSREFS Cf. A000045, A270863, A283679. Sequence in context: A124842 A134399 A094436 * A094441 A107230 A159830 Adjacent sequences: A286009 A286010 A286011 * A286013 A286014 A286015 KEYWORD nonn,tabl,more AUTHOR Oboifeng Dira, Apr 30 2017 STATUS approved

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Last modified September 23 19:57 EDT 2023. Contains 365554 sequences. (Running on oeis4.)