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A029853 Number of connected functions on n points with a loop of length 4. 3

%I

%S 1,1,4,11,35,97,282,792,2243,6275,17602,49206,137713,385208,1078667,

%T 3022342,8478199,23807190,66932592,188394855,530911452,1497892857,

%U 4230987944,11964356354,33869704270,95982410945,272279600817,773153124315,2197492308752

%N Number of connected functions on n points with a loop of length 4.

%H Andrew Howroyd, <a href="/A029853/b029853.txt">Table of n, a(n) for n = 4..500</a>

%F G.f.: A(x) = ( B(x)^4 + B(x^2)^2 + 2*B(x^4) )/4 where B(x) is the o.g.f. for A000081. - _Geoffrey Critzer_, Aug 09 2013

%F a(n) ~ A187770 * A051491^n / n^(3/2). - _Vaclav Kotesovec_, Dec 25 2020

%t nn = 20; f[x_] := Sum[a[n] x^n, {n, 0, nn}]; sol =

%t SolveAlways[

%t 0 == Series[

%t f[x] - x Product[1/(1 - x^i)^a[i], {i, 1, nn}], {x, 0, nn}],

%t x]; b = Flatten[Table[a[n], {n, 1, nn}] /. sol]; CoefficientList[

%t Series[CycleIndex[CyclicGroup[4], s] /.

%t Table[s[i] -> Sum[b[[k]] x^(k*i), {k, 1, nn}], {i, 1, 4}], {x, 0,

%t nn}], x] (* _Geoffrey Critzer_, Aug 08 2013 *)

%Y Column 4 of A339428.

%K nonn

%O 4,3

%A _Christian G. Bower_

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Last modified June 21 14:17 EDT 2021. Contains 345364 sequences. (Running on oeis4.)