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

3,1

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.

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.

Prog

(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)

Crossrefs

Cf. A100960, A291837.

Sequence in context: A195167 A364668 A211218 * A134917 A066665 A278451

Adjacent sequences: A291836 A291837 A291838 * A291840 A291841 A291842

Keyword

nonn

Author

Gheorghe Coserea, Sep 05 2017

Status

approved