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A007891 A Kutz sequence. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A133819 A274092 A021245 * A165487 A201286 A208527

Adjacent sequences:  A007888 A007889 A007890 * A007892 A007893 A007894

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 6 00:41 EDT 2021. Contains 343579 sequences. (Running on oeis4.)