OFFSET
0,5
COMMENTS
Inverse binomial transform of A091002.
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
a(n) = (3*2^n + 2*(-3)^n - 5*0^n)/30.
E.g.f.: (3*exp(2*x) + 2*exp(-3*x) - 5)/30. - G. C. Greubel, Feb 01 2019
MATHEMATICA
a[n_]:=(MatrixPower[{{1, 4}, {1, -2}}, n].{{1}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)
Join[{0, 0}, LinearRecurrence[{-1, 6}, {1, -1}, 30]] (* G. C. Greubel, Feb 01 2019 *)
CoefficientList[Series[x^2/((1-2x)(1+3x)), {x, 0, 30}], x] (* Harvey P. Dale, Apr 30 2022 *)
PROG
(PARI) vector(30, n, n--; (3*2^n + 2*(-3)^n - 5*0^n)/30) \\ G. C. Greubel, Feb 01 2019
(Magma) [0] cat [(3*2^n + 2*(-3)^n)/30: n in [1..30]]; // G. C. Greubel, Feb 01 2019
(Sage) [0] + [(3*2^n + 2*(-3)^n)/30 for n in (1..30)] # G. C. Greubel, Feb 01 2019
(GAP) Concatenation([0], List([1..30], n -> (3*2^n + 2*(-3)^n)/30)) # G. C. Greubel, Feb 01 2019
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Dec 13 2003
STATUS
approved