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 A294140 Number of total dominating sets in the n-crown graph. 0
 0, 1, 16, 121, 676, 3249, 14400, 61009, 252004, 1026169, 4145296, 16670889, 66879684, 267944161, 1072693504, 4292739361, 17175150916, 68709515625, 274856935824, 1099467588025, 4397954236900, 17591993106961, 70368341525056, 281474137850481, 1125898162012836 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS In a total dominating set each side of the crown graph requires any two vertices on the other side to dominate it. - Andrew Howroyd, Apr 16 2018 LINKS Table of n, a(n) for n=1..25. Eric Weisstein's World of Mathematics, Crown Graph Eric Weisstein's World of Mathematics, Total Dominating Set Index entries for linear recurrences with constant coefficients, signature (11,-47,101,-116,68,-16). FORMULA a(n) = (2^n - 1 - n)^2. - Andrew Howroyd, Apr 16 2018 a(n) = 11*a(n-1) - 47*a(n-2) + 101*a(n-3) - 116*a(n-4) + 68*a(n-5) -16*a(n-6). G.f.: x^2*(1 + 5*x - 8*x^2 - 4*x^3)/((-1 + x)^3*(-1 + 2*x)^2*(-1 + 4*x)). MATHEMATICA Table[(1 - 2^n + n)^2, {n, 20}] LinearRecurrence[{11, -47, 101, -116, 68, -16}, {0, 1, 16, 121, 676, 3249}, 20] CoefficientList[Series[x (1 + 5 x - 8 x^2 - 4 x^3)/((-1 + x)^3 (-1 + 2 x)^2 (-1 + 4 x)), {x, 0, 20}], x] PROG (PARI) a(n)=(2^n-1-n)^2; \\ Andrew Howroyd, Apr 16 2018 CROSSREFS Cf. A287063, A287471. Sequence in context: A017030 A082921 A191902 * A014765 A081071 A217022 Adjacent sequences: A294137 A294138 A294139 * A294141 A294142 A294143 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Apr 16 2018 EXTENSIONS a(1)-a(2) and a(11)-a(25) from Andrew Howroyd, Apr 16 2018 STATUS approved

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Last modified August 8 04:35 EDT 2024. Contains 375018 sequences. (Running on oeis4.)