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A302763
Number of minimal total dominating sets in the n-antiprism graph.
4
0, 4, 12, 28, 80, 52, 203, 524, 903, 2184, 3960, 9628, 20735, 41619, 93392, 194732, 425901, 908791, 1923408, 4177488, 8887289, 19098160, 40895771, 87444572, 187934955, 401853599, 861531618, 1846051011, 3953574901, 8476042452, 18151661911, 38898045292
OFFSET
1,2
COMMENTS
Sequence extrapolated to n=1 using recurrence. - Andrew Howroyd, Apr 15 2018
LINKS
Eric Weisstein's World of Mathematics, Antiprism Graph
Eric Weisstein's World of Mathematics, Total Dominating Set
Index entries for linear recurrences with constant coefficients, signature (0,2,4,5,8,-12,-23,-11,-11,8,37,23,-4,2,-7,-17,7,-7,-13,3,-1,-2,1).
FORMULA
G.f.: x^2*(4 + 12*x + 20*x^2 + 40*x^3 - 72*x^4 - 161*x^5 - 88*x^6 - 99*x^7 + 80*x^8 + 407*x^9 + 276*x^10 - 52*x^11 + 28*x^12 - 105*x^13 - 272*x^14 + 119*x^15 - 126*x^16 - 247*x^17 + 60*x^18 - 21*x^19 - 44*x^20 + 23*x^21)/(1 - 2*x^2 - 4*x^3 - 5*x^4 - 8*x^5 + 12*x^6 + 23*x^7 + 11*x^8 + 11*x^9 - 8*x^10 - 37*x^11 - 23*x^12 + 4*x^13 - 2*x^14 + 7*x^15 + 17*x^16 - 7*x^17 + 7*x^18 + 13*x^19 - 3*x^20 + x^21 + 2*x^22 - x^23). - Andrew Howroyd, Apr 15 2018
MATHEMATICA
Table[RootSum[-1 + 2 # + #^2 - 3 #^3 + 13 #^4 + 7 #^5 - 7 #^6 + 17 #^7 + 7 #^8 - 2 #^9 + 4 #^10 - 23 #^11 - 37 #^12 - 8 #^13 + 11 #^14 + 11 #^15 + 23 #^16 + 12 #^17 - 8 #^18 - 5 #^19 - 4 #^20 - 2 #^21 + #^23 &, #^n &], {n, 30}]
RootSum[-1 + 2 # + #^2 - 3 #^3 + 13 #^4 + 7 #^5 - 7 #^6 + 17 #^7 + 7 #^8 - 2 #^9 + 4 #^10 - 23 #^11 - 37 #^12 - 8 #^13 + 11 #^14 + 11 #^15 + 23 #^16 + 12 #^17 - 8 #^18 - 5 #^19 - 4 #^20 - 2 #^21 + #^23 &, #^Range[30] &]
LinearRecurrence[{0, 2, 4, 5, 8, -12, -23, -11, -11, 8, 37, 23, -4, 2, -7, -17, 7, -7, -13, 3, -1, -2, 1}, {0, 4, 12, 28, 80, 52, 203, 524, 903, 2184, 3960, 9628, 20735, 41619, 93392, 194732, 425901, 908791, 1923408, 4177488, 8887289, 19098160, 40895771}, 40]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Apr 12 2018
EXTENSIONS
a(1)-a(2) and terms a(11) and beyond from Andrew Howroyd, Apr 15 2018
STATUS
approved