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A115731
Permutation of natural numbers generated by 3-rowed array shown below.
1
1, 6, 2, 7, 5, 3, 12, 8, 4, 13, 11, 9, 18, 14, 10, 19, 17, 15, 24, 20, 16, 25, 23, 21, 30, 26, 22, 31, 29, 27, 36, 32, 28, 37, 35, 33, 42, 38, 34, 43, 41, 39, 48, 44, 40, 49, 47, 45, 54, 50, 46, 55, 53, 51, 60, 56, 52, 61, 59, 57, 66, 62, 58, 67, 65, 63, 72, 68, 64, 73, 71, 69
OFFSET
1,2
COMMENTS
1 6 7 12 13 18 19 24 25 ... a(n)=congruent to {0, 1} mod 6, Cf. A047225.
2 5 8 11 14 17 20 23 26 ... a(n)= 3n+2= A016789.
3 4 9 10 15 16 21 22 27 ... a(n)=congruent to {3, 4} mod 6, Cf. A047230.
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 with the term a(3), a(n+6k) = a(n) + 6k, with k>=1.
From Colin Barker, Apr 01 2018: (Start)
G.f.: x*(1 + 4*x - 8*x^2 + 13*x^3 - 15*x^4 + 13*x^5 - 5*x^6 - 4*x^7 + 4*x^8) / ((1 - x)^2*(1 - x + x^2)*(1 + x + x^2)).
a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6) for n>9.
(End)
PROG
(PARI) Vec(x*(1 + 4*x - 8*x^2 + 13*x^3 - 15*x^4 + 13*x^5 - 5*x^6 - 4*x^7 + 4*x^8) / ((1 - x)^2*(1 - x + x^2)*(1 + x + x^2)) + O(x^80)) \\ Colin Barker, Apr 01 2018
CROSSREFS
Cf. A115302.
Sequence in context: A244922 A153313 A096050 * A163340 A326823 A244381
KEYWORD
easy,nonn
AUTHOR
Giovanni Teofilatto, Mar 19 2006
STATUS
approved