A288156 Two even followed by three odd integers: the pattern is (0+2k, 0+2k, 1+2k, 1+2k, 1+2k) for k >= 0.

0, 0, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 30, 31, 31, 31, 32, 32, 33, 33, 33, 34, 34, 35, 35, 35, 36, 36, 37, 37, 37, 38, 38, 39, 39, 39, 40

Offset

0,6

Comments

a(n) = number of odd integers divisible by 5 in the interval ]2*(n-1)^2, 2*n^2[.

Links

Table of n, a(n) for n=0..100.

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

Cf. A004523.

Two zeros followed by partial sums of A232990.

Sequence in context: A214046 A085269 A173276 * A248515 A194986 A302128

Adjacent sequences: A288153 A288154 A288155 * A288157 A288158 A288159

Keyword

nonn,easy

Author

Ralf Steiner, Jun 25 2017

Status

approved