OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,10,-24).
FORMULA
G.f.: 1/((1-2*x)*(1+3*x)*(1-4*x)).
a(n) = (5*2^(2*n+3) - 7*2^(n+1) + (-1)^n*3^(n+2))/35. - Colin Barker, Dec 29 2014
a(n) = 3*a(n-1) + 10*a(n-2) - 24*a(n-3). - Colin Barker, Dec 29 2014
E.g.f.: (1/35)*(9*exp(-3*x) - 14*exp(2*x) + 40*exp(4*x)). - G. C. Greubel, Oct 10 2022
MATHEMATICA
LinearRecurrence[{3, 10, -24}, {1, 3, 19}, 41] (* G. C. Greubel, Oct 10 2022 *)
PROG
(PARI) Vec(1/((2*x-1)*(3*x+1)*(4*x-1)) + O(x^100)) \\ Colin Barker, Dec 29 2014
(Magma) [(5*2^(2*n+3) -7*2^(n+1) +(-1)^n*3^(n+2))/35: n in [0..40]]; // G. C. Greubel, Oct 10 2022
(SageMath) [(5*2^(2*n+3) -7*2^(n+1) +(-1)^n*3^(n+2))/35 for n in range(41)] # G. C. Greubel, Oct 10 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alex Ratushnyak, Dec 28 2014
STATUS
approved