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 A205248 Number of (n+1) X 2 0..1 arrays with the number of clockwise edge increases in every 2 X 2 subblock the same. 1
 16, 40, 112, 328, 976, 2920, 8752, 26248, 78736, 236200, 708592, 2125768, 6377296, 19131880, 57395632, 172186888, 516560656, 1549681960, 4649045872, 13947137608, 41841412816, 125524238440, 376572715312, 1129718145928, 3389154437776 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also, the number of cliques in the n-Apollonian network. Cliques in this graph have a maximum size of 4. - Andrew Howroyd, Sep 02 2017 LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 Eric Weisstein's World of Mathematics, Apollonian Network Eric Weisstein's World of Mathematics, Clique Index entries for linear recurrences with constant coefficients, signature (4,-3). FORMULA a(n) = 4*a(n-1) - 3*a(n-2). From Andrew Howroyd, Sep 02 2017: (Start) a(n) = 4*(3^n + 1). G.f.: 8*x*(2 - 3*x)/((1 - x)*(1 - 3*x)). a(n) = 8*A007051(n). a(n) = 1 + A289521(n) + A067771(n) + A003462(n+1) + A003462(n). (End) EXAMPLE Some solutions for n=4: 1 0 0 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 0 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 MATHEMATICA Table[4*(3^n + 1), {n, 1, 25}] (* Jean-François Alcover, Nov 01 2017, after Andrew Howroyd *) 4 (3^Range[30] + 1) (* Eric W. Weisstein, Nov 29 2017 *) LinearRecurrence[{4, -3}, {16, 40}, 30] (* Eric W. Weisstein, Nov 29 2017 *) CoefficientList[Series[-8 (-2 + 3 x)/(1 - 4 x + 3 x^2), {x, 0, 30}], x] (* Eric W. Weisstein, Nov 29 2017 *) PROG (PARI) Vec(8*(2 - 3*x)/((1 - x)*(1 - 3*x)) + O(x^40)) \\ Andrew Howroyd, Sep 02 2017 CROSSREFS Column 1 of A205255. Cf. A003462, A007051, A067771, A289521. Sequence in context: A368078 A185790 A185761 * A205186 A197903 A300901 Adjacent sequences: A205245 A205246 A205247 * A205249 A205250 A205251 KEYWORD nonn,easy AUTHOR R. H. Hardin, Jan 24 2012 STATUS approved

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Last modified March 1 12:07 EST 2024. Contains 370433 sequences. (Running on oeis4.)