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Search: id:A131213
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| A131213 |
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D_6 like six sided body centered prism as a substitution on a graph : Space group unit cell of hexagonal close packed structure ( group P6_3/mmc) characteristic polynomial is: 1008 x^4 + 2688 x^5 + 1144 x^6 - 1728 x^7 - 1129 x^8 + 360 x^9 + 303 x^10 - 24 x^11 - 31 x^12 + x^14. |
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+0
3
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| 1, 3, 8, 13, 1, 5, 12, 13, 1, 8, 12, 14, 1, 2, 3, 4, 5, 6, 14, 1, 3, 8, 13, 3, 5, 10, 13, 3, 8, 10, 14, 1, 2, 3, 4, 5, 6, 14, 1, 3, 8, 13, 1, 8, 12, 14, 3, 8, 10, 14, 7, 8, 9, 10, 11, 12, 13, 2, 6, 7, 13, 1, 3, 8, 13, 2, 4, 9, 13, 3, 5, 10, 13, 4, 6, 11, 13, 1, 5, 12, 13, 7, 8, 9, 10, 11, 12, 13, 1
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The hexagonal close packed is one of the major structures of metallic crystals and is one of the most interacting structures known, besides the cubic close packed structure Fm3m.
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FORMULA
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Substitution of the form for 4 or 7 for 12 types: a(m)={a(n),a(o),a(p)...a(z)}
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MATHEMATICA
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Clear[s] s[1] = {2, 6, 7, 13}; s[2] = {1, 3, 8, 13}; s[3] = {2, 4, 9, 13}; s[4] = {3, 5, 10, 13}; s[5] = {4, 6, 11, 13}; s[6] = {1, 5, 12, 13}; s[7] = {1, 8, 12, 14}; s[8] = {2, 7, 9, 14}; s[9] = {3, 8, 10, 14}; s[10] = {4, 9, 11, 14}; s[11] = {5, 10, 12, 14}; s[12] = {6, 7, 11, 14}; s[13] = {1, 2, 3, 4, 5, 6, 14}; s[14] = {7, 8, 9, 10, 11, 12, 13}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]]; aa = p[4]
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CROSSREFS
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Adjacent sequences: A131210 A131211 A131212 this_sequence A131214 A131215 A131216
Sequence in context: A032217 A032142 A032046 this_sequence A105371 A038188 A043361
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 27 2007
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