A367806 Inverse permutation of A160080.

0, 1, 3, 4, 6, 2, 9, 10, 12, 5, 15, 16, 18, 7, 21, 22, 24, 8, 27, 28, 30, 11, 33, 34, 36, 13, 39, 40, 42, 14, 45, 46, 48, 17, 51, 52, 54, 19, 57, 58, 60, 20, 63, 64, 66, 23, 69, 70, 72, 25, 75, 76, 78, 26, 81, 82, 84, 29, 87, 88, 90, 31, 93, 94, 96, 32, 99

Offset

0,3

Comments

Permutation of nonnegative numbers.

Links

Table of n, a(n) for n=0..66.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,-1).

Formula

a(2*n) = 3*n = A008585(n).

a(4*n+3) = 6*n+4 = A016957(n).

a(4*n+1) = A047268(n+1).

a(n) = a(n-4) + a(n-12) - a(n-16).

G.f.: (x + 3*x^2 + 4*x^3 + 6*x^4 + x^5 + 6*x^6 + 6*x^7 + 6*x^8 + 3*x^9 + 6*x^10 + 6*x^11 + 6*x^12 + x^13 + 3*x^14 + 2*x^15) / ((1 - x^4)*(1 - x^12)).

Example

As an array of four columns read by rows, the columns are A008588, A047268, A016945, A016957:
   0,  1,  3,  4;
   6,  2,  9, 10;
  12,  5, 15, 16;
  18,  7, 21, 22;
  24,  8, 27, 28;
  30, 11, 33, 34;
  ...

Mathematica

CoefficientList[Series[(x + 3*x^2 + 4*x^3 + 6*x^4 + x^5 + 6*x^6 + 6*x^7 + 6*x^8 + 3*x^9 + 6*x^10 + 6*x^11 + 6*x^12 + x^13 + 3*x^14 + 2*x^15) / ((1-x)^2*(1+x)*(1+x^2)*(1+x+x^2)*(1+x^3)*(1+x^6)), {x, 0, 66}], x] (* Stefano Spezia, Dec 27 2023 *)

Crossrefs

Cf. A008585, A008588, A016945, A016957, A047268, A160080.

Sequence in context: A214871 A055173 A261728 * A291798 A212152 A239810

Adjacent sequences: A367803 A367804 A367805 * A367807 A367808 A367809

Keyword

nonn,easy,tabf

Author

Philippe Deléham, Dec 01 2023

Status

approved