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A317613 Permutation of the nonnegative integers: lodumo_4 of A047247. 1
2, 3, 0, 1, 4, 5, 6, 7, 10, 11, 8, 9, 12, 13, 14, 15, 18, 19, 16, 17, 20, 21, 22, 23, 26, 27, 24, 25, 28, 29, 30, 31, 34, 35, 32, 33, 36, 37, 38, 39, 42, 43, 40, 41, 44, 45, 46, 47, 50, 51, 48, 49, 52, 53, 54, 55, 58, 59, 56, 57, 60, 61, 62, 63, 66, 67, 64 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Write n in base 8, then apply the following substitution to the rightmost digit: '0'->'2, '1'->'3', and vice versa. Convert back to decimal.

A self-inverse permutation: a(a(n)) = n.

Array whose columns are, in this order, A047463, A047621, A047451 and A047522, read by rows.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

OEIS wiki, Lodumo transform

Index entries for sequences that are permutations of the natural numbers

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

FORMULA

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - 2*a(n-6) + 2*a(n-7) - a(n-8), n > 7.

a(n) = (4*(floor(((2*n + 4) mod 8)/4) - floor(((n + 2) mod 8)/4)) + 2*n)/2.

a(n) = lod_4(A047247(n+1)).

a(4*n) = A047463(n+1).

a(4*n+1) = A047621(n+1).

a(4*n+2) = A047451(n+1).

a(4*n+3) = A047522(n+1).

a(A042948(n)) = A047596(n+1).

a(A042964(n+1)) = A047551(n+1).

G.f.: (x^7 + x^5 + 3*x^3 - 2*x^2 - x + 2)/(x^8 - 2*x^7 + 2*x^6 - 2*x^5 + 2*x^4 - 2*x^3 + 2*x^2 - 2*x + 1).

E.g.f.: x*exp(x) + cos(x) + sin(x) + cos(x/sqrt(2))*cosh(x/sqrt(2)) + (sqrt(2)*cos(x/sqrt(2)) - sin(x/sqrt(2)))*sinh(x/sqrt(2)).

EXAMPLE

a(25) = a('3'1') = '3'3' = 27.

a(26) = a('3'2') = '3'0' = 24.

a(27) = a('3'3') = '3'1' = 25.

a(28) = a('3'4') = '3'4' = 28.

a(29) = a('3'5') = '3'5' = 29.

The sequence as array read by rows:

  A047463, A047621, A047451, A047522;

        2,       3,       0,       1;

        4,       5,       6,       7;

       10,      11,       8,       9;

       12,      13,      14,      15;

       18,      19,      16,      17;

       20,      21,      22,      23;

       26,      27,      24,      25;

       28,      29,      30,      31;

  ...

MATHEMATICA

Table[(4*(Floor[1/4 Mod[2*n + 4, 8]] - Floor[1/4 Mod[n + 2, 8]]) + 2*n)/2, {n, 0, 100}]

f[n_] := Block[{id = IntegerDigits[n, 8]}, FromDigits[ Join[Most@ id /. {{} -> {0}}, {id[[-1]] /. {0 -> 2, 1 -> 3, 2 -> 0, 3 -> 1}}], 8]]; Array[f, 67, 0] (* or *)

CoefficientList[ Series[(x^7 + x^5 + 3x^3 - 2x^2 - x + 2)/((x - 1)^2 (x^6 + x^4 + x^2 + 1)), {x, 0, 70}], x] (* or *)

LinearRecurrence[{2, -2, 2, -2, 2, -2, 2, -1}, {2, 3, 0, 1, 4, 5, 6, 7}, 70] (* Robert G. Wilson v, Aug 01 2018 *)

PROG

(Maxima) makelist((4*(floor(mod(2*n + 4, 8)/4) - floor(mod(n + 2, 8)/4)) + 2*n)/2, n, 0, 100);

(PARI) x='x+O('x^100); Vec((x^7+x^5+3*x^3-2*x^2-x+2)/((1-x)^2*(x^6+x^4+ x^2+1))) \\ G. C. Greubel, Sep 25 2018

(MAGMA) m:=100; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((x^7+x^5+3*x^3-2*x^2-x+2)/((1-x)^2*(x^6+x^4+ x^2+1)))); // G. C. Greubel, Sep 25 2018

CROSSREFS

Cf. A047225, A047243, A047257, A064429, A080412, A159959, A026185.

Sequence in context: A163575 A275736 A276074 * A292628 A163465 A263230

Adjacent sequences:  A317610 A317611 A317612 * A317614 A317615 A317616

KEYWORD

nonn,easy,base

AUTHOR

Franck Maminirina Ramaharo, Aug 01 2018

STATUS

approved

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Last modified December 1 11:25 EST 2021. Contains 349429 sequences. (Running on oeis4.)