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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 (list; graph; refs; listen; history; text; internal format)
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

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-1).

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

Adjacent sequences: A115728 A115729 A115730 * A115732 A115733 A115734

KEYWORD

easy,nonn

AUTHOR

Giovanni Teofilatto, Mar 19 2006

STATUS

approved

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Last modified February 5 22:19 EST 2023. Contains 360087 sequences. (Running on oeis4.)