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 A358997 a(n) is the number of distinct positive real roots of the Maclaurin polynomial of degree 2*n for cos(x). 1
 0, 1, 2, 1, 2, 1, 2, 3, 2, 3, 4, 3, 4, 3, 4, 5, 4, 5, 6, 5, 6, 5, 6, 7, 6, 7, 6, 7, 8, 7, 8, 9, 8, 9, 8, 9, 10, 9, 10, 11, 10, 11, 10, 11, 12, 11, 12, 11, 12, 13, 12, 13, 14, 13, 14, 13, 14, 15, 14, 15, 14, 15, 16, 15, 16, 17, 16, 17, 16, 17, 18, 17, 18, 19, 18, 19, 18, 19, 20, 19, 20, 19, 20, 21 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS It appears that a(n) == n (mod 2) and a(n+2) - a(n) is always either 0 or 2. LINKS Robert Israel, Table of n, a(n) for n = 0..250 EXAMPLE a(2) = 2 because the Maclaurin polynomial of degree 4, 1 - x^2/2! + x^4/4!, has two distinct nonnegative real roots, namely sqrt(6-2*sqrt(3)) and sqrt(6+2*sqrt(3)). MAPLE f:= proc(n) local p, k; p:= add((-1)^k * x^k/(2*k)!, k=0..n); sturm(sturmseq(p, x), x, 0, infinity) end proc: map(f, [\$0..100]); MATHEMATICA a[n_] := CountRoots[Sum[(-1)^k*x^k/(2k)!, {k, 0, n}], {x, 0, Infinity}]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Nov 12 2023 *) CROSSREFS Cf. A012265, A332325. Sequence in context: A261641 A325622 A060145 * A373461 A257806 A035391 Adjacent sequences: A358994 A358995 A358996 * A358998 A358999 A359000 KEYWORD nonn,look AUTHOR Robert Israel, Dec 09 2022 STATUS approved

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Last modified September 8 10:03 EDT 2024. Contains 375753 sequences. (Running on oeis4.)