A007893 A Kutz sequence.

1, 4, 9, 16, 1, 4, 9, 16, 25, 4, 9, 16, 25, 36, 9, 16, 25, 36, 49, 16, 25, 36, 49, 64, 25, 36, 49, 64, 81, 36, 49, 64, 81, 100, 49, 64, 81, 100, 121, 64, 81, 100, 121, 144, 81, 100, 121, 144, 169, 100, 121, 144, 169, 196, 121, 144, 169, 196, 225, 144, 169, 196

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

Formula

The pattern is obvious!

a(n) = (n - 4*floor(n/5))^2. - Michael Somos, Jun 01 1999

G.f.: x*(1+3*x+5*x^2+7*x^3-15*x^4+x^5-x^6-3*x^7-5*x^8+9*x^9) / ((1-x)^3*(1+x+x^2+x^3+x^4)^2). - Colin Barker, Aug 05 2016

Mathematica

Table[(n - 4*Floor[n/5])^2, {n, 60}] (* Arkadiusz Wesolowski, Sep 29 2011 *)
LinearRecurrence[{1, 0, 0, 0, 2, -2, 0, 0, 0, -1, 1}, {1, 4, 9, 16, 1, 4, 9, 16, 25, 4, 9}, 80] (* or *) Join[ Range[4]^2, Flatten[Partition[Range[20]^2, 5, 1]]] (* Harvey P. Dale, May 11 2022 *)

Prog

(Magma) [(n-4*Floor(n/5))^2: n in [1..60]]; // Vincenzo Librandi, Sep 30 2011
(PARI) Vec(x*(1+3*x+5*x^2+7*x^3-15*x^4+x^5-x^6-3*x^7-5*x^8+9*x^9)/((1-x)^3*(1+x+x^2+x^3+x^4)^2) + O(x^60)) \\ Colin Barker, Aug 05 2016

Crossrefs

Sequence in context: A106548 A106546 A276191 * A070446 A258682 A070445

Adjacent sequences: A007890 A007891 A007892 * A007894 A007895 A007896

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved