The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A157235 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A157235

Number of primitive inequivalent oblique sublattices of hexagonal (triangular) lattice of index n (equivalence and symmetry of sublattices are determined using only parent lattice symmetries).
(history; published version)

#18 by Bruno Berselli at Fri Mar 19 08:48:08 EDT 2021

STATUS

reviewed

approved

#17 by Joerg Arndt at Fri Mar 19 07:51:12 EDT 2021

STATUS

proposed

reviewed

#16 by Andrey Zabolotskiy at Fri Mar 19 07:43:01 EDT 2021

STATUS

editing

proposed

#15 by Andrey Zabolotskiy at Fri Mar 19 07:39:04 EDT 2021

CROSSREFS

Cf. A003051 (all sublattices), A003050 (all primitive sublattices), A154272 (primitive sublattices fully inheriting the parent lattice symmetry, inlcuding the orientation of the mirrors), A000086 (primitive rotation-symmetric sublattices, counting mirror images as distinct), A060594 (primitive mirror-symmetric sublattices), A145377 (all sublattices inheriting the parent lattice symmetry), A304182, A000086, A060594.

#14 by Andrey Zabolotskiy at Fri Mar 19 07:30:56 EDT 2021

DATA

0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 2, 1, 3, 2, 2, 2, 5, 2, 4, 3, 5, 3, 4, 4, 6, 5, 6, 4, 10, 4, 6, 6, 8, 6, 10, 5, 9, 7, 8, 6, 14, 6, 10, 10, 11, 7, 12, 8, 14, 10, 12, 8, 17, 10, 12, 11, 14, 9, 20, 9, 15, 14, 14, 12, 22, 10, 16, 14, 22, 11, 20, 11, 18, 18, 18

KEYWORD

nonn,more,changed

EXTENSIONS

Terms a(31) and beyond from Andrey Zabolotskiy, Mar 19 2021

#13 by Andrey Zabolotskiy at Fri Mar 19 07:30:10 EDT 2021

CROSSREFS

#12 by Andrey Zabolotskiy at Fri Mar 19 07:28:48 EDT 2021

FORMULA

a(n) = A003050(n) - floor(A000086(n)-A154272(n))/2) - A060594(n). - Andrey Zabolotskiy, Mar 19 2021

#11 by Andrey Zabolotskiy at Fri Mar 19 07:24:44 EDT 2021

FORMULA

a(n) = A003050(n) - floor(A000086(n)/2) - A060594(n). - Andrey Zabolotskiy, Mar 19 2021

STATUS

approved

editing

#10 by Alois P. Heinz at Wed May 09 16:51:17 EDT 2018

STATUS

proposed

approved

#9 by Andrey Zabolotskiy at Wed May 09 16:31:05 EDT 2018

STATUS

editing

proposed