A287047 - OEIS

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A287047

a(n) is the number of rooted maps with n edges and 7 faces on an orientable surface of genus 1.

60060, 3944928, 129726760, 2908358552, 50534154408, 729734918432, 9145847808784, 102432266545800, 1046677747672360, 9908748651241088, 87930943305742512, 738178726378902064, 5905479331377981200, 45289976937922983360, 334600965220354244896, 2391127223524518889064, 16585285393291515557928 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`8,1`
	LINKS	`Table of n, a(n) for n=8..24.` `Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.`
	MATHEMATICA	`Q[0, 1, 0] = 1; Q[n_, f_, g_] /; n < 0 \|\| f < 0 \|\| g < 0 = 0;` `Q[n_, f_, g_] := Q[n, f, g] = 6/(n + 1) ((2 n - 1)/3 Q[n - 1, f, g] + (2 n - 1)/3 Q[n - 1, f - 1, g] + (2 n - 3) (2 n - 2) (2 n - 1)/12 Q[n - 2, f, g - 1] + 1/2 Sum[l = n - k; Sum[v = f - u; Sum[j = g - i; Boole[l >= 1 && v >= 1 && j >= 0] (2 k - 1) (2 l - 1) Q[k - 1, u, i] Q[l - 1, v, j], {i, 0, g}], {u, 1, f}], {k, 1, n}]);` `a[n_] := Q[n, 7, 1];` `Table[a[n], {n, 8, 24}] (* Jean-François Alcover, Oct 18 2018 *)`
	PROG	`(PARI)` `A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4x))/(2x);` `A287047_ser(N) = {` `my(y = A000108_ser(N+1));` `-4y(y-1)^8(184142y^7 + 1083793y^6 - 1540136y^5 - 1481152y^4 + 2626176y^3 - 737232y^2 - 184896y + 64320)/(y-2)^23;` `};` `Vec(A287047_ser(17))`
	CROSSREFS	`Rooted maps of genus 1 with n edges and f faces for 1<=f<=10: A002802(with offset 2) f=1, A006295 f=2, A006296 f=3, A288071 f=4, A288072 f=5, A287046 f=6, this sequence, A287048 f=8, A288073 f=9, A288074 f=10.` `Column 7 of A269921, column 1 of A270411.` `Cf. A000108.` `Sequence in context: A043635 A106774 A189985 * A075671 A186556 A205983` `Adjacent sequences: A287044 A287045 A287046 * A287048 A287049 A287050`
	KEYWORD	`nonn`
	AUTHOR	`Gheorghe Coserea, Jun 04 2017`
	STATUS	`approved`

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Last modified December 12 07:03 EST 2018. Contains 318052 sequences. (Running on oeis4.)