OFFSET
2,1
COMMENTS
Number of types of Boolean functions of n variables under a certain group.
Also the number of ordered decompositions of 2^n into 3 nonnegative integers (e.g., 2 = 0+0+2 = 0+2+0 = 2+0+0 = 1+1+0 = 1+0+1 = 0+1+1). - Tamas Kalmar-Nagy (integers(AT)kalmarnagy.com), Aug 02 2007
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 2..1000
Daniel Poveda Parrilla, Illustration of initial terms
I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.
Index entries for linear recurrences with constant coefficients, signature (7,-14,8).
FORMULA
From Ralf Stephan, Aug 23 2003: (Start)
a(n) = (3/8)*2^n + (1/32)*4^n + 1.
a(n) = (2^n+4)*(2^n+8)/32. - Tamas Kalmar-Nagy (integers(AT)kalmarnagy.com), Aug 02 2007
G.f.: 3*x^2*(1-5*x+5*x^2)/((1-x)*(1-2*x)*(1-4*x)). - Colin Barker, Mar 09 2012
a(n) = a(n-1) + 3*A000217(2^(n-3)) for n > 2. - Daniel Poveda Parrilla, Dec 27 2016
E.g.f.: (32*exp(x) + 12*exp(2*x) + exp(4*x) - 45 - 60*x)/32. - Stefano Spezia, Jul 11 2024
MATHEMATICA
Drop[#, 2] &@ CoefficientList[Series[3 x^2*(1 - 5 x + 5 x^2)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 25}], x] (* Michael De Vlieger, Jul 08 2019 *)
PROG
(Python)
def A028401(n): return ((m:=1<<n-3)+1)*((m<<1)+1) if n>2 else 3 # Chai Wah Wu, Jul 11 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Vladeta Jovovic, Feb 24 2000
Simpler definition from Tamas Kalmar-Nagy (integers(AT)kalmarnagy.com), Aug 02 2007
STATUS
approved