The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A342989 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A342989

Triangle read by rows: T(n,k) is the number of nonseparable rooted toroidal maps with n edges and k faces, n >= 2, k = 1..n-1.
(history; published version)

#16 by Michael De Vlieger at Sun Jan 02 16:09:19 EST 2022

STATUS

reviewed

approved

#15 by Michel Marcus at Sun Jan 02 13:39:39 EST 2022

STATUS

proposed

reviewed

#14 by Andrew Howroyd at Sun Jan 02 13:27:59 EST 2022

STATUS

editing

proposed

#13 by Andrew Howroyd at Sun Jan 02 13:01:28 EST 2022

LINKS

Andrew Howroyd, <a href="/A342989/b342989.txt">Table of n, a(n) for n = 2..1276</a> (first 50 rows)

STATUS

approved

editing

#12 by Susanna Cuyler at Mon Apr 05 00:07:30 EDT 2021

STATUS

proposed

approved

#11 by Andrew Howroyd at Sun Apr 04 20:33:44 EDT 2021

STATUS

editing

proposed

#10 by Andrew Howroyd at Sun Apr 04 20:26:47 EDT 2021

CROSSREFS

Row sums are A343089.

Cf. A082680 (planar case), A269921 (rooted toroidal maps), A343090, A343092.

#9 by Andrew Howroyd at Sun Apr 04 18:43:20 EDT 2021

EXAMPLE

35, 651, 1568, 651, 35;

#8 by Andrew Howroyd at Sun Apr 04 18:42:09 EDT 2021

PROG

(PARI)

MQ(n, g, x=1)={ \\ after Quadric in A269921.

my(Q=matrix(n+1, g+1)); Q[1, 1]=x;

for(n=1, n, for(g=0, min(n\2, g),

my(t = (1+x)*(2*n-1)/3 * Q[n, 1+g]

+ if(g && n>1, (2*n-3)*(2*n-2)*(2*n-1)/12 * Q[n-1, g])

+ sum(k = 1, n-1, sum(i = 0, g, (2*k-1) * (2*(n-k)-1) * Q[k, 1+i] * Q[n-k, 1+g-i]))/2);

Q[1+n, 1+g] = t * 6/(n+1); ));

Q

}

F(n, m, y, z)={my(Q=MQ(n, m, z)); sum(n=0, n, x^n*Ser(Q[1+n, ]/z, y)) + O(x*x^n)}

H(n, g=1)={my(p=F(n, g, 'y, 'z), v=Vec(polcoef(subst(p, x, serreverse(x*p^2)), g, 'y))); vector(#v, n, Vecrev(v[n], n))}

{ my(T=H(10)); for(n=1, #T, print(T[n])) }

#7 by Andrew Howroyd at Sun Apr 04 18:01:45 EDT 2021

LINKS

T. R. S. Walsh, and A. B. Lehman, <a href="http://dx.doi.org/10.1016/0095-8956(75)90050-7">Counting rooted maps by genus. III: Nonseparable maps</a>, J. Combinatorial Theory Ser. B 18 (1975), 222-259, Table II.