OFFSET
0,3
COMMENTS
It includes exclusively all the odd numbers (A005408). Except for 1, 3 and 5 that appear three times, each other odd number appears four times.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
O.g.f.: (1 + 2*x^2 - 2*x^3 + x^4 + 2*x^5 - 2*x^7)/((1 - x)^2*(1 + x + x^2 + x^3)).
E.g.f.: (3*exp(-x) + exp(x)*(7 + 2*x) - 6*cos(x) + 6*sin(x))/4 - 2*x - x^2.
a(n) = a(n-1) + a(n-4) - a(n-5) for n > 7.
a(n) = (7 + 2*n - 6*cos(n*Pi/2) + 3*(-1)^n + 6*sin(n*Pi/2))/4 for n > 2.
MATHEMATICA
LinearRecurrence[{1, 0, 0, 1, -1}, {1, 1, 3, 1, 3, 5, 7, 3}, 71]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Stefano Spezia, Oct 23 2020
STATUS
approved