A051253 Weights of rotation-symmetric functions in n variables.

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

Offset

3,2

Links

Table of n, a(n) for n=3..35.

A. Cabello, M. G. Parker, G. Scarpa and S. Severini, Exclusive disjunction structures and graph representatives of local complementation orbits, arXiv preprint arXiv:1211.4250, 2012.

A. Cabello, M. G. Parker, G. Scarpa, S. Severini, Exclusivity structures and graph representatives of local complementation orbits, (2013).

T. W. Cusick and P. Stanica, Fast Evaluation, Weights and Nonlinearity of Rotation-Symmetric Functions, Discr. Math. 258 (2002), 289-301.

Index entries for linear recurrences with constant coefficients, signature (2, 2, -2, -4).

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).

a(3)=1, a(4)=4, a(5)=6, a(6)=18, a(n) = 2*a(n-1)+2*a(n-2)-2*a(n-3)-4*a(n-4). - Harvey P. Dale, Mar 15 2015

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.

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(%);

Mathematica

LinearRecurrence[{2, 2, -2, -4}, {1, 4, 6, 18}, 40] (* Harvey P. Dale, May 05 2011 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -4, -2, 2, 2]^(n-3)*[1; 4; 6; 18])[1, 1] \\ Charles R Greathouse IV, Feb 19 2017

Crossrefs

Sequence in context: A088810 A005199 A107390 * A175955 A303526 A064403

Adjacent sequences: A051250 A051251 A051252 * A051254 A051255 A051256

Keyword

nice,easy,nonn

Author

Pantelimon Stanica (stanpan(AT)sciences.aum.edu)

Extensions

More terms from Harvey P. Dale, May 05 2011

Status

approved