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A296953
Number of bisymmetric, quasitrivial, and order-preserving binary operations on the n-element set {1,...,n}.
1
0, 1, 4, 10, 22, 46, 94, 190, 382, 766, 1534, 3070, 6142, 12286, 24574, 49150, 98302, 196606, 393214, 786430, 1572862, 3145726, 6291454, 12582910, 25165822, 50331646, 100663294, 201326590, 402653182, 805306366, 1610612734, 3221225470, 6442450942, 12884901886
OFFSET
0,3
COMMENTS
Apart from the offset the same as A033484. - R. J. Mathar, Alois P. Heinz, Jan 02 2018
FORMULA
a(0)=0, a(1)=1, a(n+1)-2*a(n) = 2.
From Colin Barker, Dec 22 2017: (Start)
G.f.: x*(1 + x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*2^(n-1) - 2 for n>0.
a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
(End)
MATHEMATICA
Nest[Append[#, 2 Last@ # + 2] &, {0, 1}, 32] (* or *)
Array[3*2^(# - 1) - 2 + Boole[# == 0]/2 &, 34, 0] (* or *)
CoefficientList[Series[x (1 + x)/((1 - x) (1 - 2 x)), {x, 0, 33}], x] (* Michael De Vlieger, Dec 22 2017 *)
PROG
(PARI) concat(0, Vec(x*(1 + x) / ((1 - x)*(1 - 2*x)) + O(x^40))) \\ Colin Barker, Dec 22 2017
CROSSREFS
Sequence in context: A265054 A099018 A033484 * A266373 A266374 A008267
KEYWORD
nonn,easy
AUTHOR
J. Devillet, Dec 22 2017
EXTENSIONS
G.f. replaced by a better g.f. by Colin Barker, Dec 23 2017
STATUS
approved