Robert W. Robinson has authored 3 sequences.
A001072
Number of minimally 2-edge-connected non-isomorphic graphs with n nodes.
Original entry on oeis.org
1, 1, 3, 4, 11, 23, 63, 159, 459, 1331, 4083, 12750
Offset: 3
- Calculated by Sridar K. Pootheri.
a(11) and a(12) added using tinygraph by
Falk Hüffner, Jan 20 2016
A007152
Evolutionary trees of magnitude n.
Original entry on oeis.org
1, 1, 4, 28, 301, 4466, 84974, 1974904, 54233540, 1718280152, 61695193880, 2475688513024, 109797950475448, 5333253012414224, 281576039542538368, 16055279332196218624, 983264280857581866112, 64369946360185677026048, 4485859513184032011682304, 331558482325457407154881024
Offset: 1
- L. R. Foulds and R. W. Robinson, Counting certain classes of evolutionary trees with singleton labels, Congress. Num., 44 (1984), 65-88.
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
-
Q := proc(n)
option remember ;
if n <= 1 then
0;
else
A007151(n)-A007151(n-1) +(n-1)*procname(n-1) ; # eq (3.5)
%/2 ;
end if;
end proc:
A007152 := proc(n)
if n = 1 then
1;
else
A007151(n-1)+Q(n-1) ; # eq (3.9)
end if ;
end proc:
seq(A007152(n),n=1..20 ); # R. J. Mathar, Mar 19 2018
-
m = 20;
A007151 = Rest[Range[0, m]! CoefficientList[ InverseSeries[ Series[(2x - E^x + 1)/(x + 1), {x, 0, m}], x], x]];
Q[n_] := Q[n] = If[n <= 1, 0, (1/2)(-A007151[[n - 1]] + A007151[[n]] + (n - 1) Q[n - 1])];
a[n_] := If[n == 1, 1, A007151[[n - 1]] + Q[n - 1]];
Array[a, m] (* Jean-François Alcover, Mar 30 2020, from Maple *)
A007151
Number of planted evolutionary trees of magnitude n.
Original entry on oeis.org
1, 3, 19, 198, 2906, 55018, 1275030, 34947664, 1105740320, 39661089864, 1590232358584, 70482038536880, 3421732373367504, 180574681050278960, 10292371442183694832, 630125771602386523392, 41239934114630205030656
Offset: 1
- L. R. Foulds and R. W. Robinson, Counting certain classes of evolutionary trees with singleton labels, Congress. Num., 44 (1984), 65-88.
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
-
A007151 := proc(n)
local k,j,i,m ,a;
if n =1 then
1;
else
a := 0 ;
for k from 1 to n-1 do
for j from 1 to k do
for i from 0 to n-1 do
for m from 0 to j do
a := a+(n+k-1)! /(k-j)! *binomial(j+i-1,j-1) *2^m *(-1)^(m+i) *combinat[stirling2](n-m+j-i-1,j-m) / m! /(n-m+j-i-1)! ;
end do:
end do:
end do:
end do:
a ;
end if;
end proc:
seq(A007151(n),n=1..10) ; # R. J. Mathar, Mar 19 2018
-
Rest[CoefficientList[InverseSeries[Series[(1 - E^x + 2*x)/(1 + x),{x,0,20}],x],x] * Range[0,20]!] (* Vaclav Kotesovec, Jan 08 2014 *)
-
a(n):=if n=1 then 1 else (sum((n+k-1)!*sum(1/((k-j)!)*sum(binomial(j+i-1,j-1)*sum((2^m*(-1)^(m+i)*stirling2(n-m+j-i-1,j-m))/(m!*(n-m+j-i-1)!),m,0,j),i,0,n-1),j,1,k),k,1,n-1)); /* Vladimir Kruchinin, Aug 07 2012 */
-
for(n=1,20, print1(if(n==1,1,sum(k=1,n-1, (n+k-1)!*sum(j=1,k, (1/(k-j)!)* sum(i=0,n-1, binomial(j+i-1,j-1)*sum(m=0,j, 2^m*(-1)^(m+i)* stirling(n-m+j-i-1,j-m,2)/(m!*(n-m+j-i-1)!)))))), ", ")) \\ G. C. Greubel, Nov 26 2017
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