A284700
Number of edge covers in the n-antiprism graph.
Original entry on oeis.org
4, 13, 205, 2902, 41413, 590758, 8427370, 120219259, 1714968133, 24464596729, 348995693650, 4978540849669, 71020558255594, 1013132129923498, 14452670295681235, 206172198577335937, 2941115696724530533, 41956003773586931038, 598516493115066264085
Offset: 0
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Table[RootSum[4 - # - 18 #^2 - 13 #^3 + #^4 &, #^n &], {n, 0, 20}] (* Eric W. Weisstein, May 17 2017 *)
LinearRecurrence[{13, 18, 1, -4}, {13, 205, 2902, 41413}, {0, 20}] (* Eric W. Weisstein, May 17 2017 *)
CoefficientList[Series[(-x^3-36*x^2-39*x+4)/(4*x^4-x^3-18*x^2-13*x+1), {x, 0, 50}], x]
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Vec((-x^3-36*x^2-39*x+4)/(4*x^4-x^3-18*x^2-13*x+1)+O(x^20)) \\ Andrew Howroyd, May 15 2017
A286911
Number of edge covers in the ladder graph P_2 x P_n.
Original entry on oeis.org
1, 7, 43, 277, 1777, 11407, 73219, 469981, 3016729, 19363879, 124293499, 797819173, 5121067777, 32871277183, 210995228083, 1354343064493, 8693301516841, 55800847838359, 358176305451691, 2299073773191541, 14757369859827601, 94725087867636847
Offset: 1
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Table[-RootSum[2 - 3 # - 6 #^2 + #^3 &, -14 #^n - 5 #^(n + 1) + #^(n + 2) &]/30, {n, 20}] (* Eric W. Weisstein, Aug 09 2017 *)
LinearRecurrence[{6, 3, -2}, {1, 7, 43}, 20] (* Eric W. Weisstein, Aug 09 2017 *)
CoefficientList[Series[(1 + x - 2 x^2)/(1 - 6 x - 3 x^2 + 2 x^3), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 09 2017 *)
A290470
Number of minimal edge covers in the n-Moebius ladder.
Original entry on oeis.org
3, 7, 15, 59, 143, 367, 1039, 2755, 7395, 20007, 53727, 144635, 389535, 1048159, 2821535, 7595267, 20443523, 55029319, 148125295, 398712379, 1073232175, 2888862159, 7776059055, 20931132355, 56341155043, 151655701607, 408217663167, 1098815603707, 2957725352255
Offset: 1
- Andrew Howroyd, Table of n, a(n) for n = 1..200
- Eric Weisstein's World of Mathematics, Edge Cover
- Eric Weisstein's World of Mathematics, Minimal Edge Cover
- Eric Weisstein's World of Mathematics, Moebius Ladder
- Index entries for linear recurrences with constant coefficients, signature (1, 2, 6, 2, 2, -2, -2, -1, 1).
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Table[2 Cos[n Pi/2] - RootSum[-1 + # + #^2 + #^3 &, #^n &] +
RootSum[1 - 2 #^2 - 2 #^3 + #^4 &, #^n &], {n, 20}]
LinearRecurrence[{1, 2, 6, 2, 2, -2, -2, -1, 1}, {3, 7, 15, 59, 143, 367, 1039, 2755, 7395}, 20]
CoefficientList[Series[-(((1 + x) (-3 - x - x^2 + x^3) (-1 - 4 x^3 + 3 x^4))/((1 + x^2) (-1 - x - x^2 + x^3) (1 - 2 x - 2 x^2 + x^4))), {x, 0, 20}], x]
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Vec((1 + x)*(1 + 4*x^3 - 3*x^4)*(3 + x + x^2 - x^3)/((1 + x^2)*(1 + x + x^2 - x^3)*(1 - 2*x - 2*x^2 + x^4)) + O(x^30)) \\ Andrew Howroyd, Aug 04 2017
Showing 1-3 of 3 results.
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