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A051253
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Weights of rotation-symmetric functions in n variables.
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2
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1, 4, 6, 18, 36, 80, 172, 360, 760, 1576, 3264, 6720, 13776, 28160, 57376, 116640, 236608, 479104, 968640, 1955712, 3944064, 7945856, 15993856, 32168448, 64656640, 129879040, 260759040, 523289088, 1049711616, 2104967168, 4219743232, 8456841216, 16944388096
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,2
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LINKS
| T. W. Cusick and P. Stanica, Fast Evaluation, Weights and Nonlinearity of Rotation-Symmetric Functions, Discr. Math. 258 (2002), 289-301.
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FORMULA
| a(n+3) = 2*a(n+1)+2*a(n)+2^n; G.f.: -[ (8*x^6)/(1-2*x)+x^3+*x^4+4*x^5 ]/(-1+2*x^2+2*x^3)
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EXAMPLE
| a(3)=1 since the rotation-symmetric function x_1*x_2*x_3 has Hamming weight 1. a(4)=4 since the rotation-symmetric function x_1*x_2*x_3+x_2*x_3*x_4+x_3*x_4*x_1+x_4*x_1*x_2 has Hamming weight 4.
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MAPLE
| t1:=(8*x^6/(1-2*x) + x^3 + 4*x^4 + 4*x^5)/(1-2*x^2-2*x^3);
t2:=series(t1, x, 40);
seriestolist(%);
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MATHEMATICA
| LinearRecurrence[{2, 2, -2, -4}, {1, 4, 6, 18}, 40] (* From Harvey P. Dale, May 05 2011 *)
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CROSSREFS
| Sequence in context: A088810 A005199 A107390 * A175955 A064403 A060667
Adjacent sequences: A051250 A051251 A051252 * A051254 A051255 A051256
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KEYWORD
| nice,easy,nonn
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AUTHOR
| Pantelimon Stanica (stanpan(AT)sciences.aum.edu)
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EXTENSIONS
| More terms from Harvey P. Dale, May 05 2011.
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