OFFSET
0,3
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,7,6).
FORMULA
G.f.: 1/((1+x)*(1+2*x)*(1-3*x)).
a(n) = ( 3^(n+2) + (2^(n+4) - 5)*(-1)^n )/20. - Colin Barker, Dec 28 2014
a(n) = 7*a(n-2) + 6*a(n-3). - Colin Barker, Dec 28 2014
E.g.f.: (9/20)*exp(3*x) + (4/5)*exp(-2*x)) - (1/4)*exp(-x). - Robert Israel, Dec 28 2014
MAPLE
seq((9/20)*3^n+(4/5)*(-2)^n-(1/4)*(-1)^n, n=0 .. 100); # Robert Israel, Dec 28 2014
MATHEMATICA
LinearRecurrence[{0, 7, 6}, {1, 0, 7}, 29] (* Jean-François Alcover, Oct 05 2017 *)
CoefficientList[Series[1/((1+x)(1+2x)(1-3x)), {x, 0, 30}], x] (* Harvey P. Dale, May 26 2020 *)
PROG
(PARI) Vec(1/((1+x)*(1+2*x)*(1-3*x)) + O(x^50)) \\ Michel Marcus, Dec 28 2014
(Magma) [(3^(n+2) + (-1)^n*(2^(n+4) - 5))/20: n in [0..50]]; // G. C. Greubel, Jul 21 2022
(SageMath) [(3^(n+2) +(-1)^n*(2^(n+4) -5))/20 for n in (0..50)] # G. C. Greubel, Jul 21 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alex Ratushnyak, Dec 27 2014
STATUS
approved