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A291839 a(n) is the minimal position at which the maximal value of row n appears in row n of triangle A100960. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A033038 A195167 A211218 * A134917 A066665 A278451

Adjacent sequences:  A291836 A291837 A291838 * A291840 A291841 A291842

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Sep 05 2017

STATUS

approved

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Last modified June 22 03:25 EDT 2021. Contains 345367 sequences. (Running on oeis4.)