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A280786 Number of topologically distinct sets of n circles with one pair intersecting. 4
1, 4, 15, 50, 162, 506, 1558, 4727, 14227, 42521, 126506, 374969, 1108476, 3269902, 9630631, 28328999, 83251569, 244471484, 717486860, 2104777227, 6172357873, 18096097750, 53044095421, 155464365080, 455601800970, 1335107222743, 3912330438784, 11464463809180, 33595343643160 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Table of n, a(n) for n=2..30.

R. J. Mathar, Topologically Distinct Sets of Non-intersecting Circles in the Plane, arXiv:1603.00077 [math.CO], 2016, row sums Table 7.

MAPLE

A280786 := proc(N)

if N < 2 then

0;

else

add(A280787(N, f), f=1..N-1) ;

end if;

end proc:

A280787 := proc(N, f)

option remember ;

local Npr, ct ;

if f = N then

return 0;

elif f = N-1 then

return 1;

elif f = 1 then

A280786(N-1)+A280788(N-2) ;

else

ct := 0 ;

for Npr from 1 to N-1 do

ct := ct+procname(Npr, 1)*A033185(N-Npr, f-1) ;

end do:

ct ;

end if;

end proc:

seq(A280786(n), n=2..30) ; # R. J. Mathar, Mar 06 2017

MATHEMATICA

a81[n_] := a81[n] = If[n <= 1, n, Sum[a81[n - j]*DivisorSum[j, #1*a81[#1] &], {j, n - 1}]/(n - 1)];

A027852[n_] := Module[{dh = 0, np}, For[np = 0, np <= n, np++, dh = a81[np]*a81[n - np] + dh]; If[EvenQ[n], dh = a81[n/2] + dh]; dh/2];

A280788[n_] := If[n == 0, 1, Sum[a81[np + 1]*A027852[n - np + 2], {np, 0, n}]];

t[n_] := t[n] = Module[{d, j}, If[n == 1, 1, Sum[Sum[d*t[d], {d, Divisors[j]}]*t[n - j], {j, 1, n - 1}]/(n - 1)]];

b[1, 1, 1] = 1;

b[n_, i_, p_] := b[n, i, p] = If[p > n, 0, If[n == 0, 1, If[Min[i, p] < 1, 0, Sum[b[n - i*j, i - 1, p - j]*Binomial[t[i] + j - 1, j], {j, 0, Min[n/i, p]}]]]]; A033185[n_, k_] := b[n, n, k];

A280786[n_] := If[n < 2, 0, Sum[A280787[n, f], {f, 1, n - 1}]];

A280787[n_, f_] := A280787[n, f] = Module[{ct}, Which[f == n, Return[0], f == n - 1, Return[1], f == 1, Return[A280786[n - 1] + A280788[n - 2]], True, ct = 0; Do[ct += A280787[np, 1]*A033185[n - np, f - 1], {np, 1, n - 1}]]; ct];

Table[A280786[n], {n, 2, 30}] (* Jean-François Alcover, Nov 23 2017, after R. J. Mathar and Alois P. Heinz *)

CROSSREFS

Row sums of A280787.

Column k=1 of A261070.

Sequence in context: A026328 A014532 A094705 * A283276 A196835 A055218

Adjacent sequences: A280783 A280784 A280785 * A280787 A280788 A280789

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 20 2017

STATUS

approved

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Last modified March 22 23:44 EDT 2023. Contains 361434 sequences. (Running on oeis4.)