A339124 a(n) is the number of squares at distance n from the central square of a golden square fractal.

1, 4, 12, 28, 60, 132, 300, 692, 1596, 3668, 8412, 19284, 44220, 101428, 232668, 533716, 1224252, 2808180, 6441372, 14775188, 33891324, 77739956, 178319964, 409030356, 938233788, 2152120564, 4936534044, 11323421716, 25973664636, 59578391604

Offset: 0

Author

Rémy Sigrist, Nov 24 2020

Keywords

• nonn
• easy

Comments

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

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..999
• Rémy Sigrist, Illustration of initial terms
• Wikipedia, Golden square fractal
• Index entries for linear recurrences with constant coefficients, signature (3,-2,0,2).

Crossrefs

See A337018 for similar sequences.

Cf. A269962 (partial sums).

Formula

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

a(0) = 1.

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

a(n) = 3*a(n-1) - 2*a(n-2) + 2*a(n-4) for n > 4. - Stefano Spezia, Dec 02 2020