A130722 The twice repeated nonnegative integers at even indices, the non-repeated nonnegative integers at odd indices.

0, 0, 0, 1, 1, 2, 1, 3, 2, 4, 2, 5, 3, 6, 3, 7, 4, 8, 4, 9, 5, 10, 5, 11, 6, 12, 6, 13, 7, 14, 7, 15, 8, 16, 8, 17, 9, 18, 9, 19, 10, 20, 10, 21, 11, 22, 11, 23, 12, 24, 12, 25, 13, 26, 13, 27, 14, 28, 14, 29, 15, 30, 15, 31, 16, 32, 16, 33, 17, 34, 17, 35, 18, 36, 18, 37, 19, 38, 19, 39

Offset

0,6

Links

Table of n, a(n) for n=0..79.

Formula

a(2*n) = A004526(n) = floor(n/2). a(2*n+1) = A001477(n) = n.

O.g.f.: (x^2+x+1)*x^3/((x-1)^2*(1+x)^2*(1+x^2)). - R. J. Mathar, Jul 07 2008

a(n) = A005044(n+2) - A005044(n-7). - Johannes W. Meijer, Oct 08 2013

a(n) = Sum_{i=1..floor(n/2)} sign((n-2i) mod 4). - Wesley Ivan Hurt, Apr 10 2018

a(n) = A106466(n-3) for n>=3. - Georg Fischer, Oct 07 2018

Maple

a := n -> A005044(n+2) - A005044(n-7): A005044 := n -> floor((1/48)*(n^2 + 3*n + 21 + (-1)^(n-1)*3*n)): seq(a(n), n=0..79); # Johannes W. Meijer, Oct 08 2013

Mathematica

Table[Sum[Sign[Mod[n - 2 i, 4]], {i, Floor[n/2]}], {n, 0, 100}] (* Wesley Ivan Hurt, Apr 10 2018 *)

Prog

(PARI) a(n) = if(n%2, n\2, n\4); \\ Altug Alkan, Apr 16 2018

Crossrefs

Cf. A001477, A004526, A005044.

Sequence in context: A289440 A290636 A106466 * A308307 A147541 A308308

Adjacent sequences: A130719 A130720 A130721 * A130723 A130724 A130725

Keyword

nonn,easy

Author

Paul Curtz, Aug 16 2007

Extensions

Edited by R. J. Mathar, Jul 07 2008

Status

approved