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Search: id:A045771
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| A045771 |
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Number of similar sublattices of index n^2 in root lattice D_4. |
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+0
2
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| 1, 1, 8, 1, 12, 8, 16, 1, 41, 12, 24, 8, 28, 16, 96, 1, 36, 41, 40, 12, 128, 24, 48, 8, 97, 28, 176, 16, 60, 96, 64, 1, 192, 36, 192, 41, 76, 40, 224, 12, 84, 128, 88, 24, 492, 48, 96, 8, 177, 97
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Multiplicative with a(2^p) = 1, a(p^e) = (e+1)*p^e + (e+1)*p^e + (2*(1+(e*p-e-1)*p^e))/((p-1)^2), p>2. Christian G. Bower (bowerc(AT)usa.net) May 21, 2005.
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LINKS
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M. Baake and R. V. Moody, Similarity submodules and root systems in four dimensions, Canad. J. Math. (1999), 51 1258-1276.
J. H. Conway, E. M. Rains and N. J. A. Sloane, On the existence of similar sublattices, Canad. J. Math. 51 (1999), 1300-1306 (Abstract, pdf, ps).
Index entries for sequences related to D_4 lattice
Index entries for sequences related to sublattices
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CROSSREFS
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Cf. A035292.
Sequence in context: A032012 A092702 A070475 this_sequence A070488 A124906 A158893
Adjacent sequences: A045768 A045769 A045770 this_sequence A045772 A045773 A045774
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KEYWORD
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nonn,mult
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AUTHOR
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Michael Baake (baake(AT)miles.math.ualberta.ca)
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