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

0,2

Comments

Permutation of the nonnegative integers.

Links

Table of n, a(n) for n=0..79.

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).

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*(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).

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

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]

Prog

(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)))

Crossrefs

Cf. A160016.

Sequence in context: A307178 A343611 A026191 * A050137 A086111 A262603

Adjacent sequences: A338203 A338204 A338205 * A338207 A338208 A338209

Keyword

nonn,easy

Author

Georg Fischer, Oct 16 2020

Status

approved