A091086 a(n) = A000975(n) mod 10.

0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0, 1, 2, 5, 0

Offset: 0

Author

Paul Barry, Dec 18 2003

Keywords

• nonn
• easy

Comments

A000975(0), A000975(1), A000975(2), A000975(3) repeating.

Links

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

Programs

Mathematica

CoefficientList[Series[x (1 + 2 x + 5 x^2)/(1 - x^4), {x, 0, 50}], x] (* G. C. Greubel, Sep 26 2017 *)
PadRight[{},120,{0,1,2,5}] (* Harvey P. Dale, Apr 30 2022 *)

PARI

x='x+O('x^50); Vec(x*(1+2*x+5*x^2)/(1-x^4)) \\ G. C. Greubel, Sep 26 2017

Formula

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

E.g.f.: 2*exp(x) - exp(-x) - cos(x) - 2*sin(x).

a(n) = 2 - (-1)^n - cos(Pi*n/2) - 2*sin(Pi*n/2).

a(n+4) = a(n). - G. C. Greubel, Sep 26 2017

2*a(n) = (n mod 2) + (n mod 4)^2. - Bruno Berselli, Oct 18 2018