A291839 a(n) is the minimal position at which the maximal value of row n appears in row n of triangle A100960.

3, 5, 7, 9, 11, 14, 16, 18, 21, 23, 25, 27, 30, 32, 34, 37, 39, 41, 43, 46, 48, 50, 52, 55, 57, 59, 61, 64, 66, 68, 71, 73, 75, 77, 80, 82, 84, 86, 89, 91, 93, 95, 98, 100, 102, 104, 107, 109, 111, 114, 116, 118, 120, 123, 125, 127, 129, 132

Offset: 3

Author

Gheorghe Coserea, Sep 05 2017

Keywords

• nonn

Links

• Gheorghe Coserea, Table of n, a(n) for n = 3..126
• E. A. Bender, Z. Gao and N. C. Wormald, The number of labeled 2-connected planar graphs, Electron. J. Combin., 9 (2002), #R43.

Crossrefs

Cf. A100960, A291837.

Programs

PARI

Q(n,k) = { \\ c-nets with n-edges, k-vertices
  if (k < 2+(n+2)\3 || k > 2*n\3, return(0));
  sum(i=2, k, sum(j=k, n, (-1)^((i+j+1-k)%2)*binomial(i+j-k,i)*i*(i-1)/2*
  (binomial(2*n-2*k+2,k-i)*binomial(2*k-2, n-j) -
  4*binomial(2*n-2*k+1, k-i-1)*binomial(2*k-3, n-j-1))));
};
A100960_ser(N) = {
my(x='x+O('x^(3*N+1)), t='t+O('t^(N+4)),
   q=t*x*Ser(vector(3*N+1, n, Polrev(vector(min(N+3, 2*n\3), k, Q(n,k)),'t))),
   d=serreverse((1+x)/exp(q/(2*t^2*x) + t*x^2/(1+t*x))-1),
   g2=intformal(t^2/2*((1+d)/(1+x)-1)));
   serlaplace(Ser(vector(N, n, subst(polcoeff(g2, n,'t),'x,'t)))*'x);
};
A291839_seq(N) = {
  my(g2=apply(Vecrev, Vec(A100960_ser(N+2))), m=apply(vecmax, g2));
  apply(v->vecmin(v)-1, vector(#g2, k, select(v->v==m[k], g2[k], 1)));
};
A291839_seq(22)

Formula

a(n) ~ c*n + o(sqrt(n)), where c=2.26287583256262... (A291840).

T(n, a(n)) = max {T(n,k), n <= k <= 3*(n-2) }, where T(n,k) is defined by A100960.