A286716 a(n) = floor(n/2) - floor((n+1)/5), n >= 0.

0, 0, 1, 1, 1, 1, 2, 2, 3, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 8, 9, 9, 10, 10, 10, 10, 11, 11, 12, 11, 12, 12, 13, 13, 13, 13, 14, 14, 15, 14, 15, 15, 16, 16, 16, 16, 17, 17, 18, 17, 18, 18, 19, 19, 19, 19, 20, 20, 21, 20, 21, 21, 22

Offset: 0

Author

Wolfdieter Lang, May 13 2017

Keywords

• nonn
• easy

Comments

This is the number of integers k in the (left-sided open) interval ((n+1)/5, floor(n/2)]. This sequence is used in A286717(n), the number of zeros of Chebyshev's S(n, x) polynomial (A049310) in the open interval (-phi, +phi), with phi = (1 + sqrt(5))/2 (golden section) = A001622.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,1,0,-1).

Crossrefs

Cf. A049310, A059169, A285870, A286717.

Programs

PARI

concat(vector(2), Vec(x^2*(1 + x + x^4) / ((1 - x)^2*(1 + x)*(1 + x + x^2 + x^3 + x^4)) + O(x^100))) \\ Colin Barker, May 18 2017

Formula

G.f.: x^2*(1 + x + x^4)/((1-x^2)*(1-x^5)).

a(n) = a(n-2) + a(n-5) - a(n-7) for n>6. - Colin Barker, May 18 2017