A380235 - OEIS

%I #11 Jan 26 2025 23:50:06

%S 1,4,2,19,16,8,106,137,128,47,709,1254,1890,1372,473,5356,12597,27036,

%T 31007,22556,7190,44558,133518,379491,611322,704066,469632,144904,

%U 397146,1464725,5229092,11017122,17691240,18521632,11990766,3534490,3716039,16373700,70805740,186044902,387965547,563764626,571333104,352456980,100895667

%N Triangle read by rows: T(n,k) is the number of n edge non-orientable genus k maps.

%H Andrew Howroyd, <a href="/A380235/b380235.txt">Table of n, a(n) for n = 1..105</a> (rows 1..14)

%H Evgeniy Krasko and Alexander Omelchenko, <a href="https://arxiv.org/abs/1712.10139">Enumeration of Unsensed Orientable Maps on Surfaces of a Given Genus</a>, arXiv:1712.10139 [math.CO], 2017, see Appendix Tables 5-7.

%H Evgeniy Krasko, <a href="https://github.com/krasko/non-orientable_maps/blob/master/G_1_to_14.txt">Maps on non-orientable surfaces</a>, 2017 (data file).

%e Triangle begins:

%e       1;

%e       4,      2;

%e      19,     16,      8;

%e     106,    137,    128,     47;

%e     709,   1254,   1890,   1372,    473;

%e    5356,  12597,  27036,  31007,  22556,   7190;

%e   44558, 133518, 379491, 611322, 704066, 469632, 144904;

%e   ...

%Y Main diagonal is A380236.

%Y Columns k=1..10 are A348802, A348803, A348804, A348805, A348806, A348807, A348808, A348809, A348810, A348811.

%Y Cf. A267180 (rooted), A379439 (on orientable surface).

%K nonn,tabl

%O 1,2

%A _Andrew Howroyd_, Jan 17 2025