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

Author

Paul Barry, May 03 2005

Keywords

• easy
• nonn

Comments

Diagonal sums of A106465.

Links

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

Programs

Mathematica

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

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