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A007893
A Kutz sequence.
1
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
R. E. Kutz, Two unusual sequences, Two-Year College Mathematics Journal, 12 (1981), 316-319.
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
KEYWORD
nonn,easy
STATUS
approved