OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Jun Wang and Zhizheng Zhang, On extensions of Calkin's binomial identities, Discrete Math., 274 (2004), 331-342.
Index entries for linear recurrences with constant coefficients, signature (6,-12,8).
FORMULA
a(n) = n*(5 + 3*n) * 2^(n-3). (See Wang and Zhang p. 333.)
From Chai Wah Wu, Jun 21 2016: (Start)
a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3) for n > 2.
G.f.: x*(2 - x)/(1 - 2*x)^3. (End)
E.g.f.: x*(4 + 3*x)*exp(2*x)/2. - Ilya Gutkovskiy, Jun 21 2016
MATHEMATICA
LinearRecurrence[{6, -12, 8}, {0, 2, 11}, 40] (* Vincenzo Librandi, Jun 22 2016 *)
PROG
(Magma) I:=[0, 2, 11]; [n le 3 select I[n] else 6*Self(n-1)-12*Self(n-2)+8*Self(n-3): n in [1..41]]; // Vincenzo Librandi, Jun 22 2016
(SageMath) [n*(5+3*n)*2^(n-3) for n in (0..40)] # G. C. Greubel, May 24 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jan 04 2004
STATUS
approved