

A289483


Number of gcdssortable tworooted graphs on n vertices such that all vertices have even degree.


0



0, 1, 1, 5, 29, 365, 7565, 259533, 16766541, 1695913805, 319025518925, 99428910374221, 53629954918196557, 51436455420773021005, 81633965668282476025165, 234346782219278654389392717, 1131832076434284133556933170509
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OFFSET

1,4


COMMENTS

This formula comes from the fact that for each possible value of the (n2)vertex subgraph G containing all of the nonroot vertices, if G has adjacency matrix A over F_2 then there are 2^rank(A) tworooted gcdssortable graphs with all vertices of even degree containing the nonroot subgraph G. Then, we can apply the formula from MacWilliams for the number of symmetric binary matrices with zero diagonal of each rank to get the total number of gcdssortable graphs with all vertices of even degree.


LINKS



FORMULA

a(n) = Sum_{s=0..floor(n/2)1} 2^((s^2+3s)/2) * (Product_{i=0..2s1} (2^(n2i)1) / Product_{i=1..s} (2^(2i)1))


MATHEMATICA

Table[Sum[2^((s^2 + 3 s)/2) * Product[(2^(n  2  i)  1), {i, 0, 2 s  1}]/Product[(2^(2 j)  1), {j, s}], {s, 0, Floor[n/2]  1}], {n, 2, 17}] (* Michael De Vlieger, Jul 12 2017 *)


PROG

(PARI) a(n) = sum(s=0, n\21, 2^((s^2+3*s)/2)*prod(i=0, 2*s1, (2^(n2i)1))/prod(i=1, s, 2^(2*i)1)); \\ Michel Marcus, Jul 07 2017


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



