OFFSET
0,3
COMMENTS
Inverse binomial transform of A091001.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-1,6).
FORMULA
G.f.: x*(1-x)/((1-2*x)*(1+3*x)).
a(n) = (3*2^n - 8*(-3)^n + 5*0^n)/30.
a(n+1) = Sum_{k=0..n} A112555(n,k)*(-3)^k. - Philippe Deléham, Sep 11 2009
E.g.f.: (3*exp(2*x) - 8*exp(-3*x) + 5)/30. - G. C. Greubel, Feb 01 2019
MATHEMATICA
CoefficientList[Series[x(1-x)/((1-2x)(1+3x)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jan 17 2017 *)
Join[{0}, LinearRecurrence[{-1, 6}, {1, -2}, 30]] (* G. C. Greubel, Feb 01 2019 *)
PROG
(PARI) vector(30, n, n--; (3*2^n - 8*(-3)^n + 5*0^n)/30) \\ G. C. Greubel, Feb 01 2019
(Magma) [0] cat [(3*2^n - 8*(-3)^n)/30: n in [1..30]]; // G. C. Greubel, Feb 01 2019
(Sage) [0] + [(3*2^n - 8*(-3)^n)/30 for n in (1..30)] # G. C. Greubel, Feb 01 2019
(GAP) Concatenation([0], List([1..30], n -> (3*2^n - 8*(-3)^n)/30)) # G. C. Greubel, Feb 01 2019
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Dec 13 2003
STATUS
approved