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

0,2

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

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

Mathematica

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

Crossrefs

Cf. A006369, A342131.

Sequence in context: A209162 A127366 A064786 * A193902 A043302 A343964

Adjacent sequences: A367283 A367284 A367285 * A367287 A367288 A367289

Keyword

nonn,easy

Author

Philippe Deléham, Nov 12 2023

Status

approved