A289195 a(n) is the number of odd integers divisible by 5 in ]4*(n-1)^2, 4*n^2[.

0, 0, 2, 2, 2, 4, 4, 6, 6, 6, 8, 8, 10, 10, 10, 12, 12, 14, 14, 14, 16, 16, 18, 18, 18, 20, 20, 22, 22, 22, 24, 24, 26, 26, 26, 28, 28, 30, 30, 30, 32, 32, 34, 34, 34, 36, 36, 38, 38, 38, 40, 40, 42, 42, 42, 44, 44, 46, 46, 46, 48, 48, 50, 50, 50, 52, 52, 54

Offset: 0

Author

Ralf Steiner, Jun 28 2017

Keywords

• nonn
• easy

Comments

This sequence has the form (0+4k,0+4k,2+4k,2+4k,2+4k) for k>=0.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Crossrefs

Cf. A289199, A289139, A289120, A289133, A289122, A288156, A004523.

Programs

Mathematica

Table[Count[Mod[Table[2(2(n-1)^2+k)-1,{k,1,4 n-2}],5],0],{n,0,50}]

PARI

concat(vector(2), Vec(2*x^2*(1 + x)*(1 - x + x^2) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)) + O(x^100))) \\ Colin Barker, Jul 04 2017

Formula

a(n + 5*k) = a(n) + 4*k.

From Colin Barker, Jul 04 2017: (Start)

G.f.: 2*x^2*(1 + x)*(1 - x + x^2) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)).

a(n) = a(n-1) + a(n-5) - a(n-6) for n>5.

(End)