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A000773
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Number of numbers == 0 (mod 3) in range 2^n to 2^(n+1) with odd number of 1's in binary expansion.
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3
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0, 0, 0, 1, 1, 6, 8, 29, 45, 130, 220, 561, 1001, 2366, 4368, 9829, 18565, 40410, 77540, 164921, 320001, 669526, 1309528, 2707629, 5326685, 10919090, 21572460, 43942081, 87087001, 176565486, 350739488, 708653429, 1410132405, 2841788170, 5662052980
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OFFSET
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1,6
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COMMENTS
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The first numbers with this property are 21, 42, 69, 81, 84, 87, 93, and 117. - T. D. Noe, Jun 20 2012
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LINKS
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FORMULA
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a(n) = (1/6)*(2^n - (-1)^n - 3^((n+1)/2)). G.f.: x^3 / ((1+x)*(1-2*x)*(1-3*x^2)). - Ralf Stephan, Aug 08 2004
a(n) = a(n-1) + 2 * a(n-2) + 3^(n/2) * (1 + (-1)^n) / 18 for all n in Z. - Michael Somos, Jan 23 2014
a(n) = - 6 * a(n-4) - 3 * a(n-3) + 5 * a(n-2) + a(n-1) for n > 4. - Hugo Pfoertner, Jun 13 2017
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EXAMPLE
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G.f. = x^4 + x^5 + 6*x^6 + 8*x^7 + 29*x^8 + 45*x^9 + 130*x^10 + 220*x^11 + ...
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MATHEMATICA
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nn = 35; CoefficientList[Series[x^3/((1 + x) (1 - 2 x) (1 - 3 x^2)), {x, 0, nn}], x] (* T. D. Noe, Jun 20 2012 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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