OFFSET
0,2
COMMENTS
Apart from initial terms, same as A008611. - Anton Chupin, Oct 24 2009
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
a(n) = Min_{i=0..n} A049604(i,n-i).
a(3n) = n, a(3n+1) = n+1, a(3n+2) = n+2 for n >= 1.
From Colin Barker, May 04 2014: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>5.
G.f.: x*(3-x-x^2-2*x^3+2*x^4) / ((1-x)^2*(1+x+x^2)). (End)
From Guenther Schrack, Nov 19 2020: (Start)
a(n) = a(n-3) + 1, for n > 4 with a(0) = 0, a(1) = 3, a(2) = 2, a(3) = 1, a(4) = 2;
a(n) = (3*n + 6 - 2*(w^(2*n)*(2 + w) + w^n*(1 - w)))/9, for n > 1 with a(0) = 0, a(1) = 3, where w = (-1 + sqrt(-3))/2, a primitive third root of unity;
a(n) = (n + 2 - 2*A057078(n))/3 for n > 1;
a(n) = A194960(n-2) for n > 2;
a(n) = (2*n + 2 - A330396(n))/3 for n > 1. (End)
MATHEMATICA
LinearRecurrence[{1, 0, 1, -1}, {0, 3, 2, 1, 2, 3}, 80] (* Harvey P. Dale, Sep 01 2018 *)
Join[{0, 3}, Table[(n+2 -2*ChebyshevU[2*n, 1/2])/3, {n, 2, 75}]] (* G. C. Greubel, Oct 22 2022 *)
PROG
(PARI) concat(0, Vec(x*(2*x^4-2*x^3-x^2-x+3)/((x-1)^2*(x^2+x+1)) + O(x^100))) \\ Colin Barker, May 04 2014
(Magma) I:=[2, 1, 2, 3]; [0, 3] cat [n le 4 select I[n] else Self(n-1) +Self(n-3) -Self(n-4): n in [1..81]]; // G. C. Greubel, Oct 22 2022
(SageMath) (Sage) [0, 3]+[(n+2 - 2*chebyshev_U(2*n, 1/2))/3 for n in (2..75)] # G. C. Greubel, Oct 22 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved