A250109 Sequence arising from study of multiplicative complexity of symmetric functions over a field with characteristic p.

-8, 0, -20, -20, -64, -48, -120, -120, -232, -208, -364, -364, -576, -544, -816, -816, -1160, -1120, -1540, -1540, -2048, -2000, -2600, -2600, -3304, -3248, -4060, -4060, -4992, -4928, -5984, -5984, -7176, -7104, -8436, -8436, -9920, -9840, -11480, -11480

Offset

1,1

Comments

No recurrence is known.

Links

Lars Blomberg, Table of n, a(n) for n = 1..5000

Maran van Heesch, The multiplicative complexity of symmetric functions over a field with characteristic p, Thesis, 2014. See Table 3.

Formula

From Lars Blomberg, Dec 04 2016: (Start)

Empirically for 5000 terms:

Let k = n mod 4.

Formula:

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

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

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

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

Recursion:

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

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

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

Crossrefs

Sequence in context: A265115 A214205 A278147 * A022900 A028652 A028636

Adjacent sequences: A250106 A250107 A250108 * A250110 A250111 A250112

Keyword

sign

Author

N. J. A. Sloane, Nov 19 2014

Extensions

More terms from Lars Blomberg, Dec 04 2016

Status

approved