OFFSET
0,2
COMMENTS
Binomial transform of (1, 5, 2, 2, 2, ...).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-5,2).
FORMULA
G.f.: (-1 - 2*x + 6*x^2)/((2*x - 1)*(x - 1)^2). - R. J. Mathar, Apr 04 2012
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). - Vincenzo Librandi, Jul 05 2012
E.g.f.: exp(x)*(2*exp(x) - 1 + 3*x). - Stefano Spezia, Mar 29 2023
EXAMPLE
a(3) = 24 = sum of row 3 terms of triangle A131832: (7 + 5 + 5 + 7).
a(3) = 24 = (1, 3, 3, 1) dot (1, 5, 2, 2) = (1 + 15 + 6 + 2).
MATHEMATICA
CoefficientList[Series[(-1-2*x+6*x^2)/((2*x-1)*(x-1)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 05 2012 *)
Table[2^(n+1)-1+3n, {n, 0, 30}] (* or *) LinearRecurrence[{4, -5, 2}, {1, 6, 13}, 40] (* Harvey P. Dale, Nov 06 2012 *)
PROG
(Magma) I:=[1, 6, 13]; [n le 3 select I[n] else 4*Self(n-1)-5*Self(n-2)+2*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jul 05 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jul 20 2007
EXTENSIONS
New definition by R. J. Mathar, Apr 04 2012
STATUS
approved