OFFSET
0,6
COMMENTS
a(n) = number of odd integers divisible by 5 in the interval ]2*(n-1)^2, 2*n^2[.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).
FORMULA
a(5*k + r) = floor((r + 3)/5) + 2*k for k >= 0 and r < 5. - David A. Corneth, Jun 25 2017
G.f.: x^2*(x^3+1)/(x^6-x^5-x+1) = x^2 *(1+x) *(1-x+x^2) /( (1-x)^2 * (1+x+x^2+x^3+x^4) ). - Alois P. Heinz, Jul 04 2017
From Luce ETIENNE, Feb 18 2020: (Start)
a(n) = 2*a(n-5) - a(n-10).
a(n) = a(n-1) + a(n-5) - a(n-6). (End)
a(n) = floor((2*n+1)/5) for n >= 0. - Mones Kasem Jaafar, Jun 25 2023
Sum_{n>=2} (-1)^n/a(n) = Pi/4. - Amiram Eldar, Jul 20 2023
MATHEMATICA
Table[Count[Mod[Table[2 ((n - 1)^2 + k) - 1, {k, 1, 2 n - 1}], 5], 0], {n, 0, 100}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ralf Steiner, Jun 25 2017
STATUS
approved