A160080 -id:A160080 - cp's OEIS frontend

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

Philippe Deléham, Dec 01 2023

Permutation of nonnegative numbers.

			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;
  ...

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).

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

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 *)

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)).

cp's OEIS Frontend

A367806 Inverse permutation of A160080.

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