A271830 Expansion of (3 - 4*x + 3*x^2 + x^4)/((1 - x)^2*(1 + x^2 + x^4)).

3, 2, 1, 4, 5, 6, 9, 8, 7, 10, 11, 12, 15, 14, 13, 16, 17, 18, 21, 20, 19, 22, 23, 24, 27, 26, 25, 28, 29, 30, 33, 32, 31, 34, 35, 36, 39, 38, 37, 40, 41, 42, 45, 44, 43, 46, 47, 48, 51, 50, 49, 52, 53, 54, 57, 56, 55, 58, 59, 60, 63, 62, 61, 64, 65, 66, 69, 68, 67, 70, 71, 72, 75, 74, 73

Offset: 0

Author

Ilya Gutkovskiy, Apr 18 2016

Keywords

• nonn
• easy

Comments

Permutation of the positive integers, with 6k+1 and 6k+3 swapped for every k.

Links

• Index entries for sequences that are permutations of the natural numbers
• Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-2,2,-1).

Crossrefs

Cf. A000027, A080412.

Programs

Magma

[3 - n + 4*Floor(n/6) + 2*Floor((n+1)/6) + 2*Floor((n+2)/6) + 4*Floor((n+3)/6) : n in [0..100]]; // Wesley Ivan Hurt, Apr 20 2016

Maple

A271830:=n->3-n+4*floor(n/6)+2*floor((n+1)/6)+2*floor((n+2)/6)+4*floor((n+3)/6): seq(A271830(n), n=0..150); # Wesley Ivan Hurt, Apr 20 2016

Mathematica

CoefficientList[Series[(3 - 4 x + 3 x^2 + x^4)/((1 - x)^2 (1 + x^2 + x^4)), {x, 0, 75}], x]
LinearRecurrence[{2, -2, 2, -2, 2, -1}, {3, 2, 1, 4, 5, 6}, 75]

PARI

x='x+O('x^99); Vec((3-4*x+3*x^2+x^4)/((1-x)^2*(1+x^2+x^4))) \\ Altug Alkan, Apr 18 2016

Formula

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

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6).

a(n) = 3 - n + 4*floor(n/6) + 2*floor((n+1)/6) + 2*floor((n+2)/6) + 4*floor((n+3)/6). - Vaclav Kotesovec, Apr 19 2016