OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..3300
Index entries for linear recurrences with constant coefficients, signature (4, -4).
FORMULA
a(n) = Sum_{k=0..n} (k+9)*binomial(n,k).
From R. J. Mathar, Apr 20 2009: (Start)
a(n) = (18+n)*2^(n-1).
a(n) = 4*a(n-1) - 4*a(n-2).
G.f.: (9-17*x)/(1-2*x)^2. (End)
a(0)=9, a(1)=19, a(n) = 4*a(n-1) - 4*a(n-2). - Harvey P. Dale, Mar 24 2013
a(n) = 2*A079862(n-10). - Michel Marcus, Sep 29 2015
E.g.f.: (x+9)*exp(2*x). - G. C. Greubel, Jun 02 2018
EXAMPLE
a(0)=9, a(1) = 2*9 + 1 = 19, a(2) = 2*19 + 2 = 40, a(3) = 2*40 + 4 = 84, a(4) = 2*84 + 8 = 176, ...
MATHEMATICA
RecurrenceTable[{a[0]==9, a[n]==2a[n-1]+2^(n-1)}, a, {n, 30}] (* or *) LinearRecurrence[{4, -4}, {9, 19}, 30] (* Harvey P. Dale, Mar 24 2013 *)
PROG
(PARI) Vec((9-17*x)/(1-2*x)^2 + O(x^40)) \\ Michel Marcus, Sep 29 2015
(Magma) I:=[9, 19]; [n le 2 select I[n] else 4*Self(n-1) - 4*Self(n-2): n in [1..30]]; // G. C. Greubel, Jun 02 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Philippe Deléham, Apr 20 2009
EXTENSIONS
More terms from Vincenzo Librandi, Apr 30 2009
STATUS
approved