OFFSET
0,2
COMMENTS
Cell configuration converges to a fractal with dimension 2.590...
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..750
Peter Karpov, InvMem, Item 26
Peter Karpov, Illustration of initial terms (n = 1..4)
Index entries for linear recurrences with constant coefficients, signature (20,-48).
FORMULA
a(0) = 1, a(1) = 7, a(2) = 116, a(n) = 20*a(n-1) - 48*a(n-2).
G.f.: (1-13*x+24*x^2)/(1-20*x+48*x^2).
a(n) = (3*(10-2*sqrt(13))^n*(13+sqrt(13)) + (2*(5+sqrt(13)))^n*(91+23*sqrt(13)))/(52*(5+sqrt(13))) for n > 0.
a(n) = (1/2)*[n=0] + (4*sqrt(3))^(n-1)*(2*sqrt(3)*ChebyshevU(n, 5/(2*sqrt(3))) - 3*ChebyshevU(n-1, 5/(2*sqrt(3)))). - G. C. Greubel, Dec 10 2021
MATHEMATICA
{1}~Join~LinearRecurrence[{20, -48}, {7, 116}, 18]
CoefficientList[Series[(1 - 13x + 24x^2)/(1 - 20x + 48x^2), {x, 0, 40}], x] (* Indranil Ghosh, Apr 19 2017 *)
PROG
(Magma) I:=[7, 116]; [n le 2 select I[n] else 20*Self(n-1) - 48*Self(n-2): n in [1..31]]; // G. C. Greubel, Dec 10 2021
(Sage) [(1/2)*bool(n==0) + (4*sqrt(3))^(n-1)*(2*sqrt(3)*chebyshev_U(n, 5/(2*sqrt(3))) - 3*chebyshev_U(n-1, 5/(2*sqrt(3)))) for n in (0..30)] # G. C. Greubel, Dec 10 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Karpov, Apr 19 2017
STATUS
approved