OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,2).
FORMULA
a(n) = 2*abs((1/2)*(-1 + (-2)^n) - (2/3)*(2 + (-2)^n)*A057427(n)).
From Colin Barker, Jan 04 2013: (Start)
a(n) = a(n-1) + 2*a(n-2) for n > 4.
G.f.: (4*x^4 + 2*x^3 + 10*x^2 - 2*x - 3) / ((x + 1)*(2*x - 1)). (End)
E.g.f.: (18 + 3*x^2 - 11*exp(-x) + 2*exp(2*x))/3. - Franck Maminirina Ramaharo, Nov 23 2018
MAPLE
seq(coeff(series((4*x^4+2*x^3+10*x^2-2*x-3)/((x+1)*(2*x-1)), x, n+1), x, n), n = 0 .. 35); # Muniru A Asiru, Nov 23 2018
MATHEMATICA
Join[{3, 5, 1}, LinearRecurrence[{1, 2}, {9, 7}, 40]] (* Harvey P. Dale, Jul 17 2014 *)
PROG
(Maxima) append([3, 5, 1], makelist((2^(1 + n) - 11*(-1)^n)/3, n, 3, 40)) /* Franck Maminirina Ramaharo, Nov 23 2018*/
(PARI) x='x+O('x^50); Vec((4*x^4+2*x^3+10*x^2-2*x-3)/((x+1)*(2*x-1))) \\ G. C. Greubel, Nov 23 2018
(Magma) I:=[9, 7]; [3, 5, 1] cat [n le 2 select I[n] else Self(n-1) + 2*Self(n-2): n in [1..45]]; // G. C. Greubel, Nov 23 2018
(Sage) s=((4*x^4+2*x^3+10*x^2-2*x-3)/((x+1)*(2*x-1))).series(x, 50); s.coefficients(x, sparse=False) # G. C. Greubel, Nov 23 2018
(GAP) a:=[3, 5, 1];; for n in [4..35] do a[n]:=(2^n-11*(-1)^(n-1))/3; od; a; # Muniru A Asiru, Nov 23 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Mar 06 2006
EXTENSIONS
a(24) corrected, new name, and editing by Colin Barker and Joerg Arndt, Jan 04 2013
STATUS
approved