A250109 - OEIS

%I #24 Apr 19 2023 19:02:27

%S -8,0,-20,-20,-64,-48,-120,-120,-232,-208,-364,-364,-576,-544,-816,

%T -816,-1160,-1120,-1540,-1540,-2048,-2000,-2600,-2600,-3304,-3248,

%U -4060,-4060,-4992,-4928,-5984,-5984,-7176,-7104,-8436,-8436,-9920,-9840,-11480,-11480

%N Sequence arising from study of multiplicative complexity of symmetric functions over a field with characteristic p.

%C No recurrence is known.

%H Lars Blomberg, <a href="/A250109/b250109.txt">Table of n, a(n) for n = 1..5000</a>

%H Maran van Heesch, <a href="https://research.tue.nl/en/studentTheses/the-multiplicative-complexity-of-symmetric-functions-over-a-field">The multiplicative complexity of symmetric functions over a field with characteristic p</a>, Thesis, 2014. See Table 3.

%F From _Lars Blomberg_, Dec 04 2016: (Start)

%F Empirically for 5000 terms:

%F Let k = n mod 4.

%F Formula:

%F k = 0: a(n) = -n*(n+1)*(n+2)/6.

%F k = 1: a(n) = -(n+3)*(n^2 + 3*n + 8)/6.

%F k = 2: a(n) = -(n-2)*(n+2)*(n+3)/6.

%F k = 3: a(n) = -(n+1)*(n+2)*(n+3)/6.

%F Recursion:

%F a(1..12) = (-8, 0, -20, -20, -64, -48, -120, -120, -232, -208, -364, -364).

%F a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12) - 64, n > 12. (End)

%F Empirical g.f.: -4*x*(2 -2*x +3*x^2 +2*x^3 +2*x^4 +x^6) / ((1 -x)^4*(1 +x)^3*(1 +x^2)^2). - _Colin Barker_, Dec 04 2016

%K sign

%O 1,1

%A _N. J. A. Sloane_, Nov 19 2014

%E More terms from _Lars Blomberg_, Dec 04 2016