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A106466 Interleave 1,2,3,.. with 1,1,2,2,3,3,... 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 4 05:54 EDT 2020. Contains 335444 sequences. (Running on oeis4.)