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 A106466 Interleave 1,2,3,.. with 1,1,2,2,3,3,... 5

%I

%S 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,

%T 8,17,9,18,9,19,10,20,10,21,11,22,11,23,12,24,12,25,13,26,13,27,14,28,

%U 14,29,15,30,15,31,16,32,16,33,17,34,17,35,18,36

%N Interleave 1,2,3,.. with 1,1,2,2,3,3,...

%C Diagonal sums of A106465.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,1,0,-1).

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

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

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

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

%F 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

%F 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

%t With[{no=36},Riffle[Range[no],Sort[Join[Range[no/2],Range[no/2]]]]] (* _Harvey P. Dale_, Feb 20 2011 *)

%K easy,nonn

%O 0,3

%A _Paul Barry_, May 03 2005

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Last modified August 15 14:58 EDT 2020. Contains 336504 sequences. (Running on oeis4.)