A043547 Odd numbers interspersed with double the previous odd number.

1, 2, 3, 6, 5, 10, 7, 14, 9, 18, 11, 22, 13, 26, 15, 30, 17, 34, 19, 38, 21, 42, 23, 46, 25, 50, 27, 54, 29, 58, 31, 62, 33, 66, 35, 70, 37, 74, 39, 78, 41, 82, 43, 86, 45, 90, 47, 94, 49, 98, 51, 102, 53, 106, 55, 110, 57, 114, 59, 118, 61, 122, 63, 126, 65, 130, 67, 134

Offset: 1

Author

Jim Cook (jcook(AT)halcyon.com), Mar 01 2000

Keywords

• easy
• nonn

Comments

As pointed out by E. Angelini on the SeqFan list (cf. link), this is the lexicographically earliest sequence of positive integers without repetitions such that the sum of four consecutive terms is always a multiple of 4. - M. F. Hasler, Mar 22 2013

Examples

			a(1)=1 because n is odd. a(2)=2 because a(1)*2=2.
		

Links

• E. Angelini, k-chunks sum and division by k, post to the SeqFan list, Mar 22 2013
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Crossrefs

For n>3, a(n) = A059029(n-3)+3. For n>1, a(n) = A022998(n-2)+2.

Programs

Magma

[n*(-1)^n/2-(-1)^n+3*n/2-1 : n in [1..50]]; // Wesley Ivan Hurt, Nov 22 2015

Maple

A043547:=n->n*(-1)^n/2-(-1)^n+3*n/2-1: seq(A043547(n), n=1..100); # Wesley Ivan Hurt, Nov 22 2015

Mathematica

Flatten[Table[Accumulate[{2 n - 1, 2 n - 1}], {n, 40}]] (* Wesley Ivan Hurt, Nov 22 2015 *)
With[{o=Range[1,71,2]},Riffle[o,2o]] (* Harvey P. Dale, Sep 17 2019 *)

PARI

A043547(n)=n+!bittest(n,0)*(n-2) \\ M. F. Hasler, Mar 22 2013

PARI

Vec(x*(1+2*x)*(1+x^2)/(1-x^2)^2 + O(x^100)) \\ Altug Alkan, Nov 22 2015

Formula

a(n) = (2 - n) * (n - floor(n/2) * 2) + 2 * (n - 1).

G.f.: x*(1+2*x)*(1+x^2)/(1-x^2)^2. - Ralf Stephan, Jun 10 2003

a(2n-1) = 2n-1, a(2n) = 4n-2. - M. F. Hasler, Mar 22 2013

From Wesley Ivan Hurt, Nov 22 2015: (Start)

a(n) = 2*a(n-2) - a(n-4) for n>4.

a(n) = n*(-1)^n/2 - (-1)^n + 3*n/2 - 1. (End)

Extensions

More terms from James Sellers, Mar 01 2000