A367286 Inverse of A342131.

0, 2, 1, 4, 6, 3, 8, 10, 5, 12, 14, 7, 16, 18, 9, 20, 22, 11, 24, 26, 13, 28, 30, 15, 32, 34, 17, 36, 38, 19, 40, 42, 21, 44, 46, 23, 48, 50, 25, 52, 54, 27, 56, 58, 29, 60, 62, 31, 64, 66, 33, 68, 70, 35, 72, 74, 37, 76, 78, 39, 80, 82, 41, 84, 86, 43, 88, 90, 45, 92, 94, 47

Offset: 0

Author

Philippe Deléham, Nov 12 2023

Keywords

• nonn
• easy

Comments

Permutation of the nonnegative numbers.

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).
• Index entries for sequences that are permutations of the nonnegative integers

Crossrefs

Cf. A006369, A342131.

Programs

Mathematica

LinearRecurrence[{0,0,2,0,0,-1},{0,2,1,4,6,3},100] (* Paolo Xausa, Nov 14 2023 *)

Formula

a(3*n) = 4*n, a(3*n+1) = 4*n+2, a(3*n+2) = 2*n+1.

a(n) = 2*a(n-3) - a(n-6) for n >= 6.

a(n) = A006369(n+1) - 1.

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

E.g.f.: exp(-x/2)*(exp(3*x/2)*(10*x + 1) + (2*x - 1)*cos(sqrt(3)*x/2) + sqrt(3)*(3 - 2*x)*sin(sqrt(3)*x/2))/9. - Stefano Spezia, Nov 12 2023