OFFSET
0,2
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-20,16).
FORMULA
G.f.: (1 - 6*x + 12*x^2)/((1 - 2*x)^2*(1 - 4*x)).
a(n) = 4*a(n-1) + 2^n*(n-2), n >= 1. - Vincenzo Librandi, Mar 13 2011
From Elmo R. Oliveira, Sep 15 2024: (Start)
E.g.f.: exp(2*x)*(exp(2*x) - 2*x).
a(n) = 8*a(n-1) - 20*a(n-2) + 16*a(n-3) for n > 2. (End)
EXAMPLE
G.f. = 1 + 2*x + 8*x^2 + 40*x^3 + 192*x^4 + 864*x^5 + 3712*x^6 + ... - Michael Somos, Jul 18 2018
MATHEMATICA
Table[4^n-n 2^n, {n, 0, 30}] (* or *) LinearRecurrence[{8, -20, 16}, {1, 2, 8}, 30] (* Harvey P. Dale, Apr 23 2017 *)
PROG
(PARI) {a(n) = 2^n * (2^n - n)}; /* Michael Somos, Jul 18 2018 */
(Magma) [4^n - n*2^n: n in [0..30]]; // G. C. Greubel, Aug 14 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 01 2011
STATUS
approved