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A380235 Triangle read by rows: T(n,k) is the number of n edge non-orientable genus k maps.

%I A380235 #11 Jan 26 2025 23:50:06
%S A380235 1,4,2,19,16,8,106,137,128,47,709,1254,1890,1372,473,5356,12597,27036,
%T A380235 31007,22556,7190,44558,133518,379491,611322,704066,469632,144904,
%U A380235 397146,1464725,5229092,11017122,17691240,18521632,11990766,3534490,3716039,16373700,70805740,186044902,387965547,563764626,571333104,352456980,100895667
%N A380235 Triangle read by rows: T(n,k) is the number of n edge non-orientable genus k maps.
%H A380235 Andrew Howroyd, <a href="/A380235/b380235.txt">Table of n, a(n) for n = 1..105</a> (rows 1..14)
%H A380235 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 A380235 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 A380235 Triangle begins:
%e A380235       1;
%e A380235       4,      2;
%e A380235      19,     16,      8;
%e A380235     106,    137,    128,     47;
%e A380235     709,   1254,   1890,   1372,    473;
%e A380235    5356,  12597,  27036,  31007,  22556,   7190;
%e A380235   44558, 133518, 379491, 611322, 704066, 469632, 144904;
%e A380235   ...
%Y A380235 Main diagonal is A380236.
%Y A380235 Columns k=1..10 are A348802, A348803, A348804, A348805, A348806, A348807, A348808, A348809, A348810, A348811.
%Y A380235 Cf. A267180 (rooted), A379439 (on orientable surface).
%K A380235 nonn,tabl
%O A380235 1,2
%A A380235 _Andrew Howroyd_, Jan 17 2025