A280786 Number of topologically distinct sets of n circles with one pair intersecting.

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

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