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
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).
Programs
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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)
Comments