A269800 -id:A269800 - cp's OEIS frontend

A280788 Convolution of A000081 and A027852, shifted by 3 leading zeros.

1, 2, 6, 15, 41, 106, 284, 750, 2010, 5382, 14523, 39290, 106854, 291552, 798675, 2194828, 6051153, 16730373, 46383002, 128910484, 359115067, 1002575810, 2804667061, 7860780578, 22070885735, 62071872704, 174842835886, 493217417610

Offset: 0

N. J. A. Sloane, Jan 20 2017

nonn

R. J. Mathar, Topologically Distinct Sets of Non-intersecting Circles in the Plane, arXiv:1603.00077 [math.CO], 2016. See (71).

Cf. A269800, A280786, A280787, A027852.

A280788 := proc(N::integer)
    if N = 0 then
        1;
    else
        add(A000081(Nprime+1)*A027852(N-Nprime+2),Nprime=0..N) ;
    end if;
end proc:
seq(A280788(n),n=0..30) ; # R. J. Mathar, Mar 06 2017

a81[n_] := a81[n] = If[n <= 1, n, Sum[a81[n - j]*DivisorSum[j, #*a81[#]&], {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}]];
Table[A280788[n], {n, 0, 27}] (* Jean-François Alcover, Nov 23 2017, from Maple *)

A280789 Triangle read by rows: number of topologically distinct sets of N circles with one pair touching, classified according to number of factors.

Original entry on oeis.org

1, 2, 1, 6, 3, 1, 16, 10, 3, 1, 46, 30, 11, 3, 1, 128, 91, 34, 11, 3, 1, 364, 268, 108, 35, 11, 3, 1, 1029, 790, 327, 112, 35, 11, 3, 1, 2930, 2308, 992, 344, 113, 35, 11, 3, 1, 8344, 6737, 2962, 1055, 348, 113, 35, 11, 3, 1

Offset: 2

N. J. A. Sloane, Jan 20 2017

			Triangle begins:
1,
2,1,
6,3,1,
16,10,3,1,
46,30,11,3,1,
128,91,34,11,3,1,
364,268,108,35,11,3,1,
1029,790,327,112,35,11,3,1,
...

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

Row sums give A269800.

cp's OEIS Frontend

A280788 Convolution of A000081 and A027852, shifted by 3 leading zeros.

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