A305381 Number of 1's in truth table for Boolean function x1 x2 x4 + x2 x3 x5 + ... + x{n-3} x{n-2} xn + x{n-2} x{n-1} x1 + x{n-1} xn x2 + xn x1 x3.

4, 6, 24, 36, 112, 184, 440, 848, 1792, 3680, 7392, 15264, 30464, 62272, 124800, 252416, 507264, 1019904, 2050048, 4111872, 8255488, 16544256, 33173504, 66454528, 133126144, 266594304, 533755904, 1068535808, 2138636288, 4280188928, 8564875264, 17137852416

Offset

4,1

Links

Robert Israel, Table of n, a(n) for n = 4..3319

Francis N. Castro, Luis A. Medina, and L. Brehsner Sepúlveda, Recursions associated to trapezoid, symmetric and rotation symmetric functions over Galois fields, arXiv preprint arXiv:1702.08038 [math.CO] (2017).

Francis N. Castro, Luis A. Medina, and L. Brehsner Sepúlveda, Recursions associated to trapezoid, symmetric and rotation symmetric functions over Galois fields, Discrete Math., 341 (2018), 1915-1931.

Index entries for linear recurrences with constant coefficients, signature (2,2,-4,0,4,-8).

Formula

a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3) + 4*a(n-5) - 8*a(n-6).

G.f.: 2*x^4*(2 - x + 2*x^2 - 4*x^3 + 8*x^4 - 16*x^5)/((1 - 2*x)*(1 - 2*x^2 - 4*x^5)). - Bruno Berselli, Jun 20 2018

Maple

f:= gfun:-rectoproc({a(n) = 2*a(n-1)+2*a(n-2)-4*a(n-3)+4*a(n-5)-8*a(n-6),
seq(a(n) = [4, 6, 24, 36, 112, 184][n+1], n=0..5)}, a(n), remember):
map(f, [$0..40]); # Robert Israel, Jun 20 2018

Mathematica

LinearRecurrence[{2, 2, -4, 0, 4, -8}, {4, 6, 24, 36, 112, 184}, 32] (* Giovanni Resta, Jun 20 2018 *)

Crossrefs

Sequence in context: A087784 A174197 A071224 * A164532 A098660 A363631

Adjacent sequences: A305378 A305379 A305380 * A305382 A305383 A305384

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 16 2018

Extensions

More terms from Giovanni Resta, Jun 20 2018

Status

approved