A332019 - OEIS

%I #15 Feb 07 2020 21:10:10

%S 1,9,21,35,48,60,72,84,96,108,120,132,144,156,168,180,192,204,216,228,

%T 240,252,264,276,288,300,312,324,336,348,360,372,384,396,408,420,432,

%U 444,456,468,480,492,504,516,528,540,552,564,576,588,600,612,624,636

%N The number of cells added in the n-th generation of the following procedure: start by coloring any triangle on the snub square tiling, then repeatedly color every cell that shares a vertex with a colored cell.

%H Peter Kagey, <a href="/A332019/b332019.txt">Table of n, a(n) for n = 1..1000</a>

%H Code Golf Stack Exchange, <a href="https://codegolf.stackexchange.com/q/198952/53884">Concentric rings on a snub square tiling</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 12*(n - 1) for n > 4.

%F From _Stefano Spezia_, Feb 05 2020: (Start)

%F G.f.: x*(1 + 7*x + 4*x^2 + 2*x^3  - x^4 - x^5)/(-1 + x)^2.

%F a(n) = 2*a(n-1) - a(n-2) for n > 6.

%F (End)

%Y Cf. A008594.

%Y A296368 is the analogous sequence when instead coloring every cell that shares a side with a colored cell.

%K easy,nonn

%O 1,2

%A _Peter Kagey_, Feb 04 2020