A339124 - OEIS

%I #16 Dec 05 2020 04:51:09

%S 1,4,12,28,60,132,300,692,1596,3668,8412,19284,44220,101428,232668,

%T 533716,1224252,2808180,6441372,14775188,33891324,77739956,178319964,

%U 409030356,938233788,2152120564,4936534044,11323421716,25973664636,59578391604

%N a(n) is the number of squares at distance n from the central square of a golden square fractal.

%C For symmetry reasons, a(n) is a multiple of 4 for any n > 0.

%H Rémy Sigrist, <a href="/A339124/b339124.txt">Table of n, a(n) for n = 0..999</a>

%H Rémy Sigrist, <a href="/A339124/a339124.png">Illustration of initial terms</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Golden_ratio#Other_properties">Golden square fractal</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,0,2).

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

%F a(0) = 1.

%F a(n) = A269962(n+1) - A269962(n) for any n > 0.

%F a(n) = 3*a(n-1) - 2*a(n-2) + 2*a(n-4) for n > 4. - _Stefano Spezia_, Dec 02 2020

%Y See A337018 for similar sequences.

%Y Cf. A269962 (partial sums).

%K nonn,easy

%O 0,2

%A _Rémy Sigrist_, Nov 24 2020