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 A001677 Number of series-parallel networks with n edges. (Formerly M0797 N0302) 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 REFERENCES 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. LINKS T. D. Noe, Table of n, a(n) for n=2..500 R. M. Foster, The number of series-parallel networks, Proc. Intern. Congr. Math., Vol. 1, 1950, p. 646. FORMULA a(n) = s(n) - (1/2)*Sum_{i=1..n-1} s(i)*s(n-i) - (1/2)*s(n/2), where s() = A000084 and the last term is omitted if n is odd. EXAMPLE a(5) = 24 - (1/2)*(1*10+2*4+4*2+10*1) = 6. MATHEMATICA 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 *) CROSSREFS Cf. A058642, A058668. Sequence in context: A151527 A086625 A152172 * A024422 A186771 A019525 Adjacent sequences:  A001674 A001675 A001676 * A001678 A001679 A001680 KEYWORD nonn,nice,easy AUTHOR EXTENSIONS More terms from David W. Wilson, Sep 20 2000 STATUS approved

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Last modified October 15 14:04 EDT 2018. Contains 316236 sequences. (Running on oeis4.)