A131042 Natural numbers A000027 with 6n+3 and 6n+4 terms swapped.

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

Offset: 1

Author

Paul Curtz, Sep 23 2007

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for sequences that are permutations of the natural numbers
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

Programs

Mathematica

LinearRecurrence[{1,0,0,0,0,1,-1},{1,2,4,3,5,6,7},80] (* Harvey P. Dale, Aug 26 2024 *)

PARI

Vec(x*(1 + x + 2*x^2 - x^3 + 2*x^4 + x^5) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x + x^2)) + O(x^100)) \\ Colin Barker, Apr 08 2017

Formula

a(n) = (24*floor(n/6)+3*n^2-3*n+8+9*floor(n/3)*(3*floor(n/3)-2*n+1)-(3*n^2-7*n+8+3*floor(n/3)*(9*floor(n/3)-6*n+7))*(-1)^floor(n/3))/4. - Luce ETIENNE, Apr 08 2017

From Colin Barker, Apr 08 2017: (Start)

G.f.: x*(1 + x + 2*x^2 - x^3 + 2*x^4 + x^5) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x + x^2)).

a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.

(End)