OFFSET
0,3
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-1,14,24).
FORMULA
G.f.: 1 / ((1+2*x)*(1+3*x)*(1-4*x)).
a(n) = ( 2^(3+2*n) + (3^(3+n)-7*2^(1+n))*(-1)^n )/21. - Colin Barker, Dec 29 2014
a(n) = -a(n-1) + 14*a(n-2) + 24*a(n-3). - Colin Barker, Dec 29 2014
E.g.f.: (1/21)*(27*exp(-3*x) - 14*exp(-2*x) + 8*exp(4*x)). - G. C. Greubel, Oct 11 2022
MATHEMATICA
LinearRecurrence[{-1, 14, 24}, {1, -1, 15}, 41] (* G. C. Greubel, Oct 11 2022 *)
PROG
(PARI) Vec(1/((1+2*x)*(1+3*x)*(1-4*x)) + O(x^50)) \\ Michel Marcus, Dec 29 2014
(Magma) [(2^(2*n+3) +(-1)^n*(3^(n+3) -7*2^(n+1)))/21: n in [0..40]]; // G. C. Greubel, Oct 11 2022
(SageMath) [(2^(2*n+3) +(-1)^n*(3^(n+3) -7*2^(n+1)))/21 for n in range(41)] # G. C. Greubel, Oct 11 2022
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Alex Ratushnyak, Dec 28 2014
STATUS
approved