login
A367806
Inverse permutation of A160080.
0
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.
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
KEYWORD
nonn,easy,tabf
AUTHOR
Philippe Deléham, Dec 01 2023
STATUS
approved