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Search: id:A102000
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| A102000 |
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Sequence generated from a lattice packing matrix. |
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+0
3
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| 1, 2, 4, 8, 32, 80, 208, 560, 1552, 4144, 11152, 30128, 81424, 219440, 592016, 1597616, 4310800, 11629616, 31377808, 84661168, 228421648
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)/a(n-1) tends to 2.698068913...an eigenvalue of M and a root of the characteristic polynomial x^4 - x^3 - 2x^2 - 4x - 8.
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LINKS
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J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, 3rd edition, 1999. (See Chap. 4.)
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FORMULA
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a(n) = right term of M^n * [1 1 1 1], where M = the 4X4 matrix that generates the D_4 lattice, [1 1 1 1 / 2 0 0 0 / 0 2 0 0 / 0 0 2 0]. a(n) = a(n-1) + 2*a(n-2) + 4*a(n-3) + 8*a(n-4), n>3.
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EXAMPLE
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a(6) = 208, since M^6 * [1 1 1 1] = [518 388 280 208].
a(6) = 208 = 80 + 2*32 + 4*8 + 8*4 = a(5) + 2*a(4) + 4*a(3) + 8*a(2).
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CROSSREFS
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Sequence in context: A053147 A128055 A061285 this_sequence A074406 A064378 A036544
Adjacent sequences: A101997 A101998 A101999 this_sequence A102001 A102002 A102003
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KEYWORD
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nonn,easy,more
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 23 2004
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