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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
Eric Weisstein's World of Mathematics, Apollonian Network
Eric Weisstein's World of Mathematics, Clique
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.
Sequence in context: A368078 A185790 A185761 * A205186 A197903 A300901
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.)