A007891 A Kutz sequence.

1, 4, 1, 4, 9, 4, 9, 16, 9, 16, 25, 16, 25, 36, 25, 36, 49, 36, 49, 64, 49, 64, 81, 64, 81, 100, 81, 100, 121, 100, 121, 144, 121, 144, 169, 144, 169, 196, 169, 196, 225, 196, 225, 256, 225, 256, 289, 256, 289, 324, 289, 324, 361, 324, 361, 400, 361, 400, 441

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

R. E. Kutz, Two unusual sequences, Two-Year College Mathematics Journal, 12 (1981), 316-319.

Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1).

Formula

a(n) = (n-2*floor(n/3))^2. - Arkadiusz Wesolowski, Sep 28 2011

From Colin Barker, Aug 05 2016: (Start)

a(n) = a(n-1)+2*a(n-3)-2*a(n-4)-a(n-6)+a(n-7) for n>7.

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

(End)

Mathematica

Table[(n - 2*Floor[n/3])^2, {n, 60}] (* Arkadiusz Wesolowski, Sep 29 2011 *)

Prog

(Magma) [(n-2*Floor(n/3))^2: n in [1..60]]; // Vincenzo Librandi, Sep 30 2011
(PARI) a(n)=(n-n\3*2)^2 \\ Charles R Greathouse IV, Aug 05 2016
(PARI) Vec(x*(1+3*x-3*x^2+x^3-x^4+x^5)/((1-x)^3*(1+x+x^2)^2) + O(x^60)) \\ Colin Barker, Aug 05 2016

Crossrefs

Sequence in context: A274092 A349039 A021245 * A165487 A344685 A201286

Adjacent sequences: A007888 A007889 A007890 * A007892 A007893 A007894

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved