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A316316
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Coordination sequence for tetravalent node in chamfered version of square grid.
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4
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1, 4, 8, 8, 12, 20, 20, 20, 28, 32, 32, 36, 40, 44, 48, 48, 52, 60, 60, 60, 68, 72, 72, 76, 80, 84, 88, 88, 92, 100, 100, 100, 108, 112, 112, 116, 120, 124, 128, 128, 132, 140, 140, 140, 148, 152, 152, 156, 160, 164, 168, 168, 172, 180, 180, 180, 188, 192, 192
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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FORMULA
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Apparently, a(n + 12) = a(n) + 40 for any n > 0. - Rémy Sigrist, Jun 30 2018
Theorem: a(n + 12) = a(n) + 40 for any n > 0.
The proof uses the Coloring Book Method described in the Goodman-Strauss - Sloane article. For details see the two links.
G.f.: (1 + 3*x + 5*x^2 + 2*x^3 + 5*x^4 + 3*x^5 + x^6) / ((1 - x)^2*(1 + x^2)*(1 + x + x^2)).
a(n) = a(n-1) - a(n-2) + 2*a(n-3) - a(n-4) + a(n-5) - a(n-6) for n>6.
(End)
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MATHEMATICA
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Join[{1}, LinearRecurrence[{1, -1, 2, -1, 1, -1}, {4, 8, 8, 12, 20, 20}, 100]] (* Jean-François Alcover, Dec 13 2018 *)
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PROG
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(PARI) See Links section.
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CROSSREFS
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See A250120 for links to thousands of other coordination sequences.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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