A302763 Number of minimal total dominating sets in the n-antiprism graph.
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
Keywords
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..200
- Eric Weisstein's World of Mathematics, Antiprism Graph.
- Eric Weisstein's World of Mathematics, Minimal 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).
Programs
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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]
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
Extensions
a(1)-a(2) and terms a(11) and beyond from Andrew Howroyd, Apr 15 2018
Comments