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 A226951 Number of filiform Lie algebras with a certain grading of dimension n over Z_2. 1
 1, 1, 2, 4, 4, 6, 6, 10, 10, 16, 14, 20, 18, 26, 20, 32, 28, 36, 32, 44, 40, 56, 46, 56, 54, 74, 60, 82, 64, 84, 68, 86, 74, 100, 84, 106, 92, 114, 98, 126, 104, 126, 112, 138, 122, 156, 134, 152, 140, 170, 142, 172, 152, 194, 176, 188, 170, 222, 196, 232, 184 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,3 COMMENTS Let G = be a filiform Lie algebra of dimension n over Z_2. Define the grading [X_i,X_j]=c_(i,j)X_(i+j), for i,j >=2 for some constants c_(i,j) in Z_2. How many such algebras there exist on dimension n? The sequence gives us up to a point this numbers starting with dimension four, that is, there exists only one such an algebra with dimension four, 1 again with dimension 5, 2 with dimension 6 and so forth. LINKS John Tsartsaflis, Table of n, a(n) for n = 4..254 Grant Cairns, Ana Hinić Galić, and Yuri Nikolayevsky, Totally geodesic subalgebras of nilpotent Lie algebras, arxiv.org 1112.1288 John Tsartsaflis, Maple implementation M. Vergne, Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes, Bull. Soc. Math. France 98 (1970), 81-116. CROSSREFS Sequence in context: A164798 A087554 A281072 * A251557 A231901 A135974 Adjacent sequences:  A226948 A226949 A226950 * A226952 A226953 A226954 KEYWORD nonn AUTHOR John Tsartsaflis, Jun 24 2013 STATUS approved

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Last modified June 18 18:52 EDT 2019. Contains 324215 sequences. (Running on oeis4.)