A106450 a(n) = A004443(n) if n is odd, a(n) = A004443(n)/2 if n is even.

2, 3, 0, 1, 3, 7, 2, 5, 5, 11, 4, 9, 7, 15, 6, 13, 9, 19, 8, 17, 11, 23, 10, 21, 13, 27, 12, 25, 15, 31, 14, 29, 17, 35, 16, 33, 19, 39, 18, 37, 21, 43, 20, 41, 23, 47, 22, 45, 25, 51, 24, 49, 27, 55, 26, 53, 29, 59, 28, 57, 31, 63, 30, 61, 33, 67, 32, 65, 35, 71, 34, 69, 37, 75

Offset: 0

Author

Antti Karttunen, May 21 2005

Keywords

• nonn
• easy

Links

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

Crossrefs

Skipping the initial term (a(0)=2), this is row 2 of A106449.

Programs

PARI

Vec((2+3*x-2*x^2-2*x^3+x^4+3*x^5+x^6)/((1-x)^2*(1+x)^2*(1+x^2)) + O(x^50)) \\ Colin Barker, Apr 19 2016

Formula

a(4*n+1) = 4*n+3, a(4*n+2) = 2*n, a(4*n+3) = 4*n+1, a(4*n+4) = 2*n+3.

From Colin Barker, Apr 19 2016: (Start)

a(n) = ((2+4*i)*(-i)^n+(2-4*i)*i^n-(-3+(-1)^n)*n)/4 for n>0 where i is the imaginary unit.

a(n) = a(n-2)+a(n-4)-a(n-6) for n>6.

G.f.: (2+3*x-2*x^2-2*x^3+x^4+3*x^5+x^6) / ((1-x)^2*(1+x)^2*(1+x^2)).

(End)

From Ilya Gutkovskiy, Apr 19 2016: (Start)

a(n) = (4*floor(1/(n+1)) - (-1)^n*n + 3*n + 8*sin((Pi*n)/2) + 4*cos((Pi*n)/2))/4.

E.g.f.: 1 + cos(x) + x*cosh(x) + 2*sin(x) + x*sinh(x)/2. (End)