A106466 Interleave 1,2,3,.. with 1,1,2,2,3,3,...

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

Offset

0,3

Comments

Diagonal sums of A106465.

Links

Table of n, a(n) for n=0..70.

Index entries for linear recurrences with constant coefficients, signature (0,1,0,1,0,-1).

Formula

G.f.: (1+x+x^2)/((1+x^2)(1-x^2)^2);

a(n) = a(n-2) + a(n-4) - a(n-6);

a(n) = Sum_{k=0..floor(n/2)} (gcd(n-k+1, k+1) mod 2);

a(n) = sin(Pi*n/2)/4 + (n+2)*(-1)^n/8 + 3(n+2)/8;

a(n) = 0^n + Sum_{k=0..n-1} (if(k=floor((n-1)/2) or k=floor(n/2),1,0)*floor((k+2)/2)). - Paul Barry, Nov 22 2009

Also, a(n) = ((3 + (-1)^n)*(n+2) - i*(i^n - (-i)^n))/8, where i is the imaginary unit. - Bruno Berselli, Feb 22 2010

Mathematica

With[{no=36}, Riffle[Range[no], Sort[Join[Range[no/2], Range[no/2]]]]]  (* Harvey P. Dale, Feb 20 2011 *)

Crossrefs

Sequence in context: A214270 A289440 A290636 * A130722 A308307 A147541

Adjacent sequences: A106463 A106464 A106465 * A106467 A106468 A106469

Keyword

easy,nonn

Author

Paul Barry, May 03 2005

Status

approved