OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,3,0,3,0,4).
FORMULA
a(n+1) - 2*a(n) = A135575(n).
O.g.f.: x^2*(3 + x +2*x^2 +3*x^3)/((1-2*x)*(1+2*x)*(x^2-x+1)*(x^2+x+1)). - R. J. Mathar, Mar 31 2008
a(n) = 3*a(n-2) + 3*a(n-4) + 4*a(n-6). - G. C. Greubel, Oct 19 2016
a(n) = (1/6)*(2^(n-1)*(5+3*(-1)^n) - (1+3*(-1)^n)*ChebyshevU(n, 1/2) - (1-3*(-1)^n)*ChebyshevU(n-1, 1/2)). - G. C. Greubel, Jan 05 2022
MAPLE
MATHEMATICA
LinearRecurrence[{0, 3, 0, 3, 0, 4}, {0, 0, 3, 1, 11, 6}, 41] (* G. C. Greubel, Oct 19 2016 *)
PROG
(Magma) I:=[0, 0, 3, 1, 11, 6]; [n le 6 select I[n] else 3*Self(n-2) +3*Self(n-4) +4*Self(n-6): n in [1..41]]; // G. C. Greubel, Jan 05 2022
(Sage) [(1/6)*(2^(n-1)*(5+3*(-1)^n) - (1+3*(-1)^n)*chebyshev_U(n, 1/2) - (1-3*(-1)^n)*chebyshev_U(n-1, 1/2)) for n in (0..40)] # G. C. Greubel, Jan 05 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Feb 24 2008
EXTENSIONS
More terms from R. J. Mathar, Mar 31 2008
More terms from R. J. Mathar, Feb 07 2009
STATUS
approved