| NAME
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allocated for Eric W. Weisstein
Number of minimum total dominating sets in the n-path graph.
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| DATA
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0, 1, 2, 1, 1, 4, 3, 1, 2, 9, 4, 1, 3, 16, 5, 1, 4, 25, 6, 1, 5, 36, 7, 1, 6, 49, 8, 1, 7, 64, 9, 1, 8, 81, 10, 1, 9, 100, 11, 1, 10, 121, 12, 1, 11, 144, 13, 1, 12, 169, 14, 1, 13, 196, 15, 1, 14, 225, 16, 1, 15, 256, 17, 1, 16, 289, 18, 1, 17, 324, 19, 1, 18, 361, 20, 1
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| OFFSET
|
1,3
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| LINKS
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Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PathGraph.html">Path Graph</a>
Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotalDominatingSet.html">Total Dominating Set</a>
<a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1).
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| FORMULA
|
a(n) = ((-1)^n*(n - 2)^2 + (6 + n)^2 - 2*(n - 2)*(n + 6)*cos(n*Pi/2) - 48*sin(n*Pi/2))/6.
a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12).
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| MATHEMATICA
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Table[Piecewise[{{1, Mod[n, 4] == 0}, {((n + 2)/4)^2, Mod[n, 4] == 2}, {(n - 1)/4, Mod[n, 4] == 1}, {(n + 5)/4, Mod[n, 4] == 3}}], {n, 20}]
Table[((-1)^n (n - 2)^2 + (6 + n)^2 - 2 (n - 2) (n + 6) Cos[n Pi/2] - 48 Sin[n Pi/2])/64, {n, 20}]
LinearRecurrence[{0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1}, {0, 1, 2, 1, 1, 4, 3, 1, 2, 9, 4, 1}, 20]
|
| KEYWORD
|
allocated
nonn
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| AUTHOR
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Eric W. Weisstein, Apr 11 2018
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| STATUS
|
approved
editing
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|