

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
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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)(1x^2)^2);
a(n) = a(n2) + a(n4)  a(n6);
a(n) = Sum_{k=0..floor(n/2)} (gcd(nk+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..n1} (if(k=floor((n1)/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



