The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A302658

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A302658

Number of minimal total dominating sets in the wheel graph on n nodes.
(history; published version)

#20 by Alois P. Heinz at Mon Apr 16 15:39:41 EDT 2018

STATUS

reviewed

approved

#19 by Wesley Ivan Hurt at Mon Apr 16 15:02:41 EDT 2018

STATUS

proposed

reviewed

#18 by Wesley Ivan Hurt at Mon Apr 16 15:02:33 EDT 2018

STATUS

editing

proposed

#17 by Wesley Ivan Hurt at Mon Apr 16 15:02:07 EDT 2018

MATHEMATICA

Table[n - 1 + RootSum[-1 - # + #^3 &, #^(n - 1) &] + (1 - (-1)^n) RootSum[-1 + #^2 + #^3 &, #^((n - 1)/2) &], {n, 2, 3050}]

LinearRecurrence[{2, -1, 1, -1, 0, 0, -1, 0, 1, 1, -1}, {1, 2, 6, 8, 10, 15, 14, 12, 21, 35, 33}, 2050]

CoefficientList[Series[(1 + 3 x^2 - 3 x^3 - x^4 - x^5 - 8 x^6 - 2 x^7 + 8 x^8 + 11 x^9 - 9 x^10)/((-1 + x)^2 (1 - x^3 - x^4 - x^5 - x^6 + x^8 + x^9)), {x, 0, 2050}], x]

STATUS

proposed

editing

#16 by Eric W. Weisstein at Mon Apr 16 13:57:59 EDT 2018

STATUS

editing

proposed

#15 by Eric W. Weisstein at Mon Apr 16 13:57:56 EDT 2018

LINKS

<a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-1,0,0,-1,0,1,1,-1).

FORMULA

G.f.: x^2*(1 + 3*x^2 - 3*x^3 - x^4 - x^5 - 8*x^6 - 2*x^7 + 8*x^8 + 11*x^9 - 9*x^10)/((-1 + x)^2*(1 - x^3 - x^4 - x^5 - x^6 + x^8 + x^9)).

MATHEMATICA

Table[n - 1 + RootSum[-1 - # + #^3 &, #^(n - 1) &] + (1 - (-1)^n) RootSum[-1 + #^2 + #^3 &, #^((n - 1)/2) &], {n, 2, 30}]

LinearRecurrence[{2, -1, 1, -1, 0, 0, -1, 0, 1, 1, -1}, {1, 2, 6, 8, 10, 15, 14, 12, 21, 35, 33}, 20]

CoefficientList[Series[(1 + 3 x^2 - 3 x^3 - x^4 - x^5 - 8 x^6 - 2 x^7 + 8 x^8 + 11 x^9 - 9 x^10)/((-1 + x)^2 (1 - x^3 - x^4 - x^5 - x^6 + x^8 + x^9)), {x, 0, 20}], x]

STATUS

approved

editing

#14 by N. J. A. Sloane at Sun Apr 15 21:51:19 EDT 2018

STATUS

proposed

approved

#13 by Andrew Howroyd at Sun Apr 15 17:54:21 EDT 2018

STATUS

editing

proposed

#12 by Andrew Howroyd at Sun Apr 15 17:42:51 EDT 2018

COMMENTS

Sequence extrapolated Wheel graphs are defined for n>=4; extended to n=2 using formula. - _Andrew Howroyd_, Apr 15 2018

#11 by Andrew Howroyd at Sun Apr 15 17:40:53 EDT 2018

EXTENSIONS

Terms a(2)-a(3) and terms a(20) and beyond from Andrew Howroyd, Apr 15 2018