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 A302652 Number of minimum total dominating sets in the n-antiprism graph. 4
 2, 6, 12, 24, 80, 48, 7, 16, 237, 40, 154, 1344, 208, 7, 30, 1136, 68, 396, 6688, 480, 7, 44, 3151, 96, 750, 20800, 864, 7, 58, 6730, 124, 1216, 50160, 1360, 7, 72, 12321, 152, 1794, 103040, 1968, 7, 86, 20372, 180, 2484, 189504, 2688, 7, 100, 31331, 208, 3286 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Sequence extrapolated to n=1 using recurrence. 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, Total Dominating Set Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 1). FORMULA From Andrew Howroyd, Apr 18 2018: (Start) a(n) = 5*a(n-7) - 10*a(n-14) + 10*a(n-21) - 5*a(n-28) + a(n-35). a(7k) = 7, a(7k+1) = 2*(7*k+1), a(7k+2) = (7*k+2)*(32*k^2+38*k+9)/3, a(7k+3) = 4*(7*k+3), a(7k+4) = (7*k+4)*(8*k+6), a(7k+5) = (7*k+5)*(8*k+8)*(k+2)*(4*k+3)/3, a(7k+6) = 8*(7*k+6)*(k+1). (End) MATHEMATICA Table[Piecewise[{{7, Mod[n, 7] == 0}, {2 n, Mod[n, 7] == 1}, {n (37 + 138 n + 32 n^2)/147, Mod[n, 7] == 2}, {4 n, Mod[n, 7] == 3}, {2 n (5 + 4 n)/7, Mod[n, 7] == 4}, {(8 n (2 + n) (9 + n) (1 + 4 n))/1029, Mod[n, 7] == 5}, {8 n (1 + n)/7, Mod[n, 7] == 6}}, {n, 200}] LinearRecurrence[{0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 1}, {2, 6, 12, 24, 80, 48, 7, 16, 237, 40, 154, 1344, 208, 7, 30, 1136, 68, 396, 6688, 480, 7, 44, 3151, 96, 750, 20800, 864, 7, 58, 6730, 124, 1216, 50160, 1360, 7}, 200] Rest @ CoefficientList[Series[7 x^7/(1 - x^7) - 16 x^6 (3 + 4 x^7)/(-1 + x^7)^3 + 4 x^3 (3 + 4 x^7)/(-1 + x^7)^2 + 2 x (1 + 6 x^7)/(-1 + x^7)^2 - 2 x^4 (12 + 41 x^7 + 3 x^14)/(-1 + x^7)^3 - 16 x^5 (5 + 59 x^7 + 48 x^14)/(-1 + x^7)^5 + x^2 (6 + 213 x^7 + 224 x^14 + 5 x^21)/(-1 + x^7)^4, {x, 0, 200}], x] PROG (PARI) a(n)={[k->7, k->2*(7*k+1), k->(7*k+2)*(32*k^2+38*k+9)/3, k->4*(7*k+3), k->(7*k+4)*(8*k+6), k->(7*k+5)*(8*k+8)*(k+2)*(4*k+3)/3, k->8*(7*k+6)*(k+1)][1+n%7](n\7)} \\ Andrew Howroyd, Apr 18 2018 CROSSREFS Cf. A302255, A302760, A302763. Sequence in context: A335327 A163895 A309016 * A180071 A034882 A175943 Adjacent sequences:  A302649 A302650 A302651 * A302653 A302654 A302655 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Apr 11 2018 EXTENSIONS a(1)-a(2) and terms a(15) and beyond from Andrew Howroyd, Apr 18 2018 STATUS approved

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Last modified May 15 10:54 EDT 2021. Contains 343909 sequences. (Running on oeis4.)