A058668
Number of unlabeled graphs with n edges, no nodes of degree 1 and no cut nodes, under "series-equivalence"; multiple edges are allowed.
Original entry on oeis.org
0, 1, 2, 5, 6, 13, 28
Offset: 1
- B. D. H. Tellegen, Geometrical configurations and duality of electrical networks, Philips Technical Review, 5 (1940), 324-330.
A001677
Number of series-parallel networks with n edges.
Original entry on oeis.org
1, 2, 3, 6, 12, 26, 59, 146, 368, 976, 2667, 7482, 21440, 62622, 185637, 557680, 1694256, 5198142, 16086486, 50165218, 157510504, 497607008, 1580800091, 5047337994, 16190223624, 52153429218, 168657986843, 547389492416
Offset: 2
a(5) = 24 - (1/2)*(1*10+2*4+4*2+10*1) = 6.
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- B. D. H. Tellegen, Geometrical configurations and duality of electrical networks, Philips Technical Review, 5 (1940), 324-330.
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m = 29; ClearAll[a, b, s]; a[1] = 1; a[2] = 2; a[3] = 4; b[1] = 1; b[n_ /; n >= 2] = a[n]/2; ex = Product[ 1/(1-x^k)^b[k], {k, 1, m}] - 1 - Sum[ a[k]*x^k, {k, 1, m}]; coes = CoefficientList[ Series[ ex, {x, 0, m}], x]; sol = Solve[ Thread[ coes == 0]][[1]]; Do[ s[k] = a[k] /. sol, {k, 1, m}]; a[2] = 1; a[3] = 2; a[n_] := s[n] - (1/2)*Sum[ s[i]*s[n-i], {i, 1, n-1}] - If[ OddQ[n], 0, s[n/2]/2]; Table[ a[n], {n, 2, m}] (* Jean-François Alcover, Feb 24 2012 *)
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