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A290937 Number of unrooted 4-regular one-face maps on genus g surface. 0
1, 6, 510, 169772, 120644422, 144369379620, 260893265836244, 663907896121296616, 2263925904300525582790, 9968065754464730977513732, 55061782851836038471634743076, 372905924364031740449809951518408, 3038839062713596039129776983675546524, 29335649951838749853328539549957507066456, 331082145356452130774665205463914398071175024 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Evgeniy Krasko, Alexander Omelchenko, Enumeration of 4-regular one-face maps, European Journal of Combinatorics, Volume 62, 2017, Pages 167-177. Summation limit "floor(g/2+r_4/4)" in Formula (14) should read "floor(g/2-r_4/4)".
EXAMPLE
On a torus (g=1) there exists only one unrooted 4-regular one-face map. On a double torus (g=2) there are 6 such maps.
PROG
(Python 2.7)
import math
fact = math.factorial
def a(g):
s = 0
s += 2 * fact(4 * g - 2) / (4 ** g * fact(g) * fact(g - 1))
s += 3 * fact(4 * g - 2) / (fact (2 * g + 1) * fact(2 * g - 2))
s += sum((4 * g - 2) * fact(2 * g - 2 * g_ + k - 1) / (fact(2 * k - 4 * g_ + 2) * fact(g_) * fact(k - g_) * fact (2 * g - 1 - 2 * k)) for g_ in range(1, g / 2 + 1) for k in range(2 * g_ - 1, g))
s += sum((4 * g - 2) * 2 ** (2 * g_ - 2 + r4) * fact(k - 2 * g_ + g - r4 / 2) / (fact(g_) * fact(k - g_) * fact(g - r4 / 2 - 2 * k) * fact(2 * k + 3 - 4 * g_ - r4) * fact(r4 - 1)) for g_ in range(g / 4 + 1) for r4 in range(2, 2 * (g + 3 - 4 * g_) / 3 + 1, 2) for k in range(2 * g_ - 1 + r4 / 2, (2 * g - r4) / 4 + 1))
return s / (8 * g - 4)
CROSSREFS
Rooted maps: A290819.
Sequence in context: A272094 A103520 A223050 * A364482 A365926 A250391
KEYWORD
nonn
AUTHOR
Evgeniy Krasko, Sep 03 2017
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)