OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,2,-24).
FORMULA
G.f.: 1/((1+2*x)*(1-3*x)*(1-4*x)).
a(n) = ((-1)^n*2^(n+1) + 5*2^(2*n+3) - 3^(n+3))/15. - Colin Barker, Dec 29 2014
a(n) = 5*a(n-1) + 2*a(n-2) - 24*a(n-3). - Colin Barker, Dec 29 2014
E.g.f.: (1/15)*(2*exp(-2*x) - 27*exp(3*x) + 40*exp(4*x)). - G. C. Greubel, Oct 10 2022
MATHEMATICA
LinearRecurrence[{5, 2, -24}, {1, 5, 27}, 41] (* G. C. Greubel, Oct 10 2022 *)
CoefficientList[Series[1/((1+2x)(1-3x)(1-4x)), {x, 0, 40}], x] (* Harvey P. Dale, Oct 28 2022 *)
PROG
(PARI) Vec(1/((1+2*x)*(1-3*x)*(1-4*x)) + O(x^50)) \\ Michel Marcus, Dec 29 2014
(Magma) [(5*2^(2*n+3) +(-1)^n*2^(n+1) -3^(n+3))/15: n in [0..40]]; // G. C. Greubel, Oct 10 2022
(SageMath) [(5*2^(2*n+3) +(-1)^n*2^(n+1) -3^(n+3))/15 for n in range(41)] # G. C. Greubel, Oct 10 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alex Ratushnyak, Dec 28 2014
STATUS
approved