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 A302650 Number of minimal total dominating sets in the n-barbell graph. 1
 1, 1, 6, 28, 85, 201, 406, 736, 1233, 1945, 2926, 4236, 5941, 8113, 10830, 14176, 18241, 23121, 28918, 35740, 43701, 52921, 63526, 75648, 89425, 105001, 122526, 142156, 164053, 188385, 215326, 245056, 277761, 313633, 352870, 395676, 442261, 492841, 547638, 606880 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Extended to a(1)-a(2) using the formula/recurrence. LINKS Eric Weisstein's World of Mathematics, Barbell Graph Eric Weisstein's World of Mathematics, Total Dominating Set Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1). FORMULA a(n) = (2 + (n - 3)*n*(n + 1)/4)*n. G.f.: x*(-1 + 4*x - 11*x^2 + 2*x^3)/(-1 + x)^5. a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). MATHEMATICA Table[(2 + (n - 3) n (n + 1)/4) n, {n, 20}] LinearRecurrence[{5, -10, 10, -5, 1}, {1, 1, 6, 28, 85}, 20] CoefficientList[Series[(-1 + 4 x - 11 x^2 + 2 x^3)/(-1 + x)^5, {x, 0, 20}], x] CROSSREFS Sequence in context: A279915 A300906 A222198 * A055711 A141255 A091321 Adjacent sequences:  A302647 A302648 A302649 * A302651 A302652 A302653 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Apr 11 2018 STATUS approved

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Last modified June 22 04:06 EDT 2021. Contains 345367 sequences. (Running on oeis4.)