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A106466
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Interleave 1,2,3,.. with 1,1,2,2,3,3,...
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2
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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; internal format)
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OFFSET
| 0,3
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COMMENTS
| Diagonal sums of A106465.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (0,1,0,1,0,-1).
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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)}. [From Paul Barry (pbarry(AT)wit.ie), 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
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MATHEMATICA
| With[{no=36}, Riffle[Range[no], Sort[Join[Range[no/2], Range[no/2]]]]] (* From Harvey P. Dale, Feb 20 2011 *)
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CROSSREFS
| Sequence in context: A123021 A028914 A204539 * A130722 A147541 A024162
Adjacent sequences: A106463 A106464 A106465 * A106467 A106468 A106469
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 03 2005
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