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A295495 Number of dissections of an n-gon by nonintersecting diagonals into polygons with a prime number of sides counted up to rotations. 5
1, 1, 2, 5, 11, 36, 114, 410, 1458, 5488, 20786, 80770, 317378, 1265139, 5094139, 20718347, 84961256, 351086326, 1460591637, 6113826319, 25733864299, 108867782794, 462707558813, 1974991841442, 8463121111860, 36397780088126, 157066702354947, 679917566925030 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 3..200

E. Krasko, A. Omelchenko, Brown's Theorem and its Application for Enumeration of Dissections and Planar Trees, The Electronic Journal of Combinatorics, 22 (2015), #P1.17.

PROG

(PARI) \\ number of dissections into parts defined by set.

DissectionsModCyclic(v)={my(n=#v);

my(q=vector(n)); q[1]=serreverse(x-sum(i=3, #v, x^i*v[i])/x + O(x*x^n));

for(i=2, n, q[i]=q[i-1]*q[1]);

my(vars=variables(q[1]));

my(u(m, r)=substvec(q[r]+O(x^(n\m+1)), vars, apply(t->t^m, vars)));

my(p=O(x*x^n) + x*u(1, 1) - x^2 + (u(2, 1)-u(1, 2))/2 + sum(i=3, #v, my(c=v[i]); if(c, c*sumdiv(i, d, eulerphi(d)*u(d, i/d))/i)));

vector(n, i, polcoeff(p, i))}

DissectionsModCyclic(apply(i->isprime(i), [1..30]))

CROSSREFS

Cf. A003455, A295224, A295419.

Sequence in context: A101834 A117758 A284251 * A130622 A112600 A156014

Adjacent sequences:  A295492 A295493 A295494 * A295496 A295497 A295498

KEYWORD

nonn

AUTHOR

Andrew Howroyd, Nov 22 2017

STATUS

approved

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Last modified March 25 01:17 EDT 2019. Contains 321450 sequences. (Running on oeis4.)