A007892 A Kutz sequence.

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

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