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A007892 A Kutz sequence. 2
1, 4, 9, 1, 4, 9, 16, 4, 9, 16, 25, 9, 16, 25, 36, 16, 25, 36, 49, 25, 36, 49, 64, 36, 49, 64, 81, 49, 64, 81, 100, 64, 81, 100, 121, 81, 100, 121, 144, 100, 121, 144, 169, 121, 144, 169, 196, 144, 169, 196, 225, 169, 196, 225, 256, 196, 225, 256, 289, 225 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The pattern is obvious: after the initial three terms, we have four successive squares.

Another description of the same sequence: array read by rows, with four columns, in which row n lists n^2, (n+1)^2, (n+2)^2, n^2. - Omar E. Pol, Sep 28 2011

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 (1,0,0,2,-2,0,0,-1,1).

FORMULA

a(n) = (floor((-1)^n+(n+5)/2)-3*floor((n+6)/4))^2. [Arkadiusz Wesolowski, Sep 27 2011]

a(n) = (n-3*floor(n/4))^2. [Arkadiusz Wesolowski, Sep 28 2011]

G.f.: x*(1+3*x+5*x^2-8*x^3+x^4-x^5-3*x^6+4*x^7)/((1-x)^3*(1+x+x^2+x^3)^2). a(n) = (A110657(n-1)+1)^2 = ((2*n-6*(-1)^((n-1)*n/2)-3*(-1)^n+9)/8)^2. [Bruno Berselli, Sep 28 2011]

MATHEMATICA

Table[(n - 3*Floor[n/4])^2, {n, 60}] (* Arkadiusz Wesolowski, Sep 29 2011 *)

Rest[Flatten[Table[Range[n, n+3]^2, {n, 0, 20}]]] (* Harvey P. Dale, Oct 24 2015 *)

PROG

(MAGMA) [(n-3*Floor(n/4))^2: n in [1..60]]; // Vincenzo Librandi, Sep 28 2011

(PARI) a(n)=(floor((-1)^n+(n+5)/2)-3*floor((n+6)/4))^2 \\ Charles R Greathouse IV, Sep 28 2011

(Maxima) makelist(((2*n-6*(-1)^((n-1)*n/2)-3*(-1)^n+9)/8)^2, n, 1, 60); \\ Bruno Berselli, Sep 28 2011

CROSSREFS

Sequence in context: A011290 A196502 A129971 * A010297 A001191 A120865

Adjacent sequences:  A007889 A007890 A007891 * A007893 A007894 A007895

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 18 15:21 EDT 2019. Contains 328162 sequences. (Running on oeis4.)