A131739 a(4n) = a(4n+1) = n, a(4n+2) = 3n+2, a(4n+3) = 3n+3.

0, 0, 2, 3, 1, 1, 5, 6, 2, 2, 8, 9, 3, 3, 11, 12, 4, 4, 14, 15, 5, 5, 17, 18, 6, 6, 20, 21, 7, 7, 23, 24, 8, 8, 26, 27, 9, 9, 29, 30, 10, 10, 32, 33, 11, 11, 35, 36, 12, 12, 38, 39, 13, 13, 41, 42, 14, 14, 44, 45, 15, 15, 47, 48, 16, 16, 50, 51, 17, 17, 53, 54, 18, 18, 56, 57, 19, 19, 59

Offset

0,3

Links

Table of n, a(n) for n=0..78.

Index entries for linear recurrences with constant coefficients, signature (2,-3,4,-3,2,-1).

Formula

From Chai Wah Wu, Mar 20 2017: (Start)

a(n) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 3*a(n-4) + 2*a(n-5) - a(n-6) for n > 5.

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

From Luce ETIENNE, Apr 08 2017: (Start)

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

a(n) = (2*n+1-(n+1)*cos(n*Pi/2)-(n+2)*sin(n*Pi/2))/4. (End)

Mathematica

Table[Switch[Mod[n, 4], 0, n/4, 1, (n - 1)/4, 2, 3 (n - 2)/4 + 2, _, 3 (n - 3)/4 + 3], {n, 0, 78}] (* or *)
CoefficientList[Series[x^2*(x^2 - x + 2)/((x - 1)^2*(x^2 + 1)^2), {x, 0, 78}], x] (* Michael De Vlieger, Mar 20 2017 *)
LinearRecurrence[{2, -3, 4, -3, 2, -1}, {0, 0, 2, 3, 1, 1}, 100] (* Harvey P. Dale, Mar 26 2023 *)

Crossrefs

Sequence in context: A166029 A049278 A194680 * A011151 A140878 A182933

Adjacent sequences: A131736 A131737 A131738 * A131740 A131741 A131742

Keyword

nonn

Author

Paul Curtz, Sep 19 2007

Status

approved