A338206 Inverse of permutation in A160016.

0, 2, 1, 6, 3, 10, 4, 14, 5, 18, 7, 22, 8, 26, 9, 30, 11, 34, 12, 38, 13, 42, 15, 46, 16, 50, 17, 54, 19, 58, 20, 62, 21, 66, 23, 70, 24, 74, 25, 78, 27, 82, 28, 86, 29, 90, 31, 94, 32, 98, 33, 102, 35, 106, 36, 110, 37, 114, 39, 118, 40, 122, 41, 126, 43, 130, 44, 134, 45, 138, 47, 142, 48, 146, 49, 150, 51, 154, 52, 158

Offset: 0

Author

Georg Fischer, Oct 16 2020

Keywords

• nonn
• easy

Comments

Permutation of the nonnegative integers.

Links

• Index entries for sequences that are permutations of the natural numbers
• Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,0,1,0,-1).

Crossrefs

Cf. A160016.

Programs

Maple

gf := (x*(1 + x^2)*(2 + x + 2*x^2 + x^3 + 2*x^4))/((-1 + x)^2*(1 + x)^2*(1 - x + x^2)*(1 + x + x^2)): ser := series(gf, x, 82):
seq(coeff(ser, x, n), n=0..79); # Peter Luschny, Oct 16 2020

Mathematica

LinearRecurrence[{0,1,0,0,0,1,0,-1}, {0,2,1,6,3,10,4,14},80]

PARI

my(x='x+O('x^80)); Vec((x*(2+x+4*x^2+2*x^3+4*x^4+x^5+2*x^6))/((1-x^2)^2*(1+x^2+x^4)))

Formula

Blocks of 6 numbers: a(6*k+0 .. 6*k+5) = (4*k+0, 12*k+2, 4*k+1, 12*k+6, 4*k+3, 12*k+10) for k >= 0.

O.g.f.: x*(1 + x^2)*(2 + x + 2*x^2 + x^3 + 2*x^4)/((1 - x^2)^2*(1 + x^2 + x^4)).

If n is odd, then a(n) = 2*n; otherwise, a(n) = nearest integer to 2*n/3. - Philippe Deléham, Nov 09 2023