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
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
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Jan 24 2012
STATUS
approved