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A116551
Permutation of natural numbers generated by 3-rowed array shown below.
1
0, 3, 1, 6, 4, 2, 9, 7, 5, 12, 10, 8, 15, 13, 11, 18, 16, 14, 21, 19, 17, 24, 22, 20, 27, 25, 23, 30, 28, 26, 33, 31, 29, 36, 34, 32, 39, 37, 35, 42, 40, 38, 45, 43, 41, 48, 46, 44, 51, 49, 47, 54, 52, 50, 57, 55, 53, 60, 58, 56, 63, 61, 59, 66, 64, 62, 69, 67, 65, 72, 70, 68, 75
OFFSET
1,2
COMMENTS
0 3 6 9 12 15 18 21 24 ... a(n)= 3n
1 4 7 10 13 16 19 22 25 ... a(n)= 3n+1
2 5 8 11 14 17 20 23 26 ... a(n)= 3n+2
REFERENCES
M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988.
Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta, UTET, CittaStudiEdizioni, Milano 1997.
FORMULA
Starting at the term a(3), a(n+3k) = a(n) + 3k, with k>=1.
From Chai Wah Wu, Jul 10 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n > 7.
G.f.: x^2*(2*x^5 - 5*x^3 + 5*x^2 - 2*x + 3)/(x^4 - x^3 - x + 1). (End)
MATHEMATICA
Rest[CoefficientList[Series[x^2*(2*x^5 - 5*x^3 + 5*x^2 - 2*x + 3)/(x^4 - x^3 - x + 1), {x, 0, 50}], x]] (* or *) Join[{0, 3, 1, 6, 4, 2, 9}, LinearRecurrence[{1, 0, 1, -1}, {7, 5, 12, 10}, 50]] (* G. C. Greubel, Sep 20 2017 *)
PROG
(PARI) x='x+O('x^50); Vec(x^2*(2*x^5 - 5*x^3 + 5*x^2 - 2*x + 3)/(x^4 - x^3 - x + 1)) \\ G. C. Greubel, Sep 20 2017
CROSSREFS
Cf. A115302.
Sequence in context: A209165 A121437 A078585 * A213783 A163330 A370394
KEYWORD
easy,nonn
AUTHOR
Giovanni Teofilatto, Mar 17 2006
STATUS
approved