cp's OEIS Frontend

A245519 Number of alpha-labeled graphs with n edges and at most n vertices.

%I A245519 #33 May 03 2020 14:42:09
%S A245519 0,0,0,2,10,64,336,1872,11104,71944,508032,3511232,27192704,223750464,
%T A245519 1947253504,17899536448,173156535168,1760383827776,18752453106176,
%U A245519 209034916385472,2432351796434560,29509268795249700
%N A245519 Number of alpha-labeled graphs with n edges and at most n vertices.
%H A245519 Christian Barrientos, Sarah Minion, <a href="https://dx.doi.org/10.7151/dmgt.1985">On the number of alpha-labeled graphs</a>, Discussiones Mathematicae Graph Theory, to appear.
%H A245519 J. A. Gallian, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/DS6">A dynamic survey of graph labeling</a>, Elec. J. Combin., (2013), #DS6.
%H A245519 David A. Sheppard, <a href="http://dx.doi.org/10.1016/0012-365X(76)90051-0">The factorial representation of major balanced labelled graphs</a>, Discrete Math., 15(1976), no. 4, 379-388.
%F A245519 a(n) = Sum_{L=1..n-2} Sum_{i=1..n-1} Product_{k=1..n} d(L,k,i), where
%F A245519 for i < L,
%F A245519             d(L,k)       if 1 <= k <= i,
%F A245519 d(L,k,i) ={ d(L,k) - 1   if i < k < n - i,
%F A245519             d(L,k)       if n - i <= k <= n;
%F A245519 for i > L + 1,
%F A245519             d(L,k)       if 1 <= k <= n - i,
%F A245519 d(L,k,i) ={ d(L,k) - 1   if n - i < k < n - i + L + 2,
%F A245519             d(L,k)       if n - i + L + 2 <= k <= n.
%F A245519           k          if 1 <= k < m,
%F A245519 d(L,k) ={ L + 1      if m <= k <= M,
%F A245519           n + 1 - k  if M < k <= n,
%F A245519 m = min{L + 1, n - L}, M = max{L + 1, n - L}.
%e A245519 For n=4, a(4)=2, there are 2 alpha-labeled graphs with 4 edges and at most 4 vertices.
%e A245519 For n=10, a(10)=71944, there are 71944 alpha-labeled graphs with 10 edges and at most 10 vertices.
%Y A245519 Cf. A241094, A005193.
%K A245519 nonn,easy
%O A245519 1,4
%A A245519 _Sarah Minion_ and _Christian Barrientos_, Jul 24 2014