OFFSET
0,4
COMMENTS
Binomial transform of A091005.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,5,-6).
FORMULA
G.f.: x^2/((1-x)*(1+2*x)*(1-3*x)).
a(n) = (3^(n+1) - (-2)^(n+1) - 5)/30.
a(n) = Sum_{k=1..n} binomial(n-k, k)*6^(k-1). - Zerinvary Lajos, Sep 30 2006
E.g.f.: (3*exp(3*x) + 2*exp(-2*x) - 5*exp(x))/30. - G. C. Greubel, Feb 01 2019
MAPLE
a:=n->sum(binomial(n-k, k)*6^(k-1), k=1..n): seq(a(n), n=0..27); # Zerinvary Lajos, Sep 30 2006
MATHEMATICA
Table[(3^n -(-2)^n - 5)/30, {n, 40}] (* Vladimir Joseph Stephan Orlovsky, Jun 20 2011 *)
LinearRecurrence[{2, 5, -6}, {0, 0, 1}, 30] (* G. C. Greubel, Feb 01 2019 *)
PROG
(Sage) from sage.combinat.sloane_functions import recur_gen2b; it = recur_gen2b(1, 2, 1, 6, lambda n: 1); [next(it) for i in range(0, 29)] # Zerinvary Lajos, Jul 03 2008
(Sage) [(3^(n+1) - (-2)^(n+1) - 5)/30 for n in range(30)] # G. C. Greubel, Feb 01 2019
(PARI) vector(30, n, n--; (3^(n+1) - (-2)^(n+1) - 5)/30) \\ G. C. Greubel, Feb 01 2019
(Magma) [(3^(n+1) - (-2)^(n+1) - 5)/30: n in [0..30]]; // ~~~
(GAP) List([0..30], n -> (3^(n+1) - (-2)^(n+1) - 5)/30) # G. C. Greubel, Feb 01 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Dec 12 2003
STATUS
approved