OFFSET
0,2
COMMENTS
n-th difference of a(n), a(n-1), ..., a(0) is (8, 16, 24, ...).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-8,4).
FORMULA
a(n) = 8*n * 2^(n-1) + 1.
a(n) = 5*a(n-1)-8*a(n-2)+4*a(n-3) for n>2. G.f.: (1+4*x-4*x^2) / ((1-x)*(1-2*x)^2). - Colin Barker, Feb 18 2016
a(n) = Sum_{k=0..n+2} Sum_{i=0..n+2} C(n+1,i) - C(k,i). - Wesley Ivan Hurt, Sep 21 2017
MATHEMATICA
Table[8 n*2^(n - 1) + 1, {n, 0, 29}] (* or *)
CoefficientList[Series[(1 + 4 x - 4 x^2)/((1 - x) (1 - 2 x)^2), {x, 0, 29}], x] (* Michael De Vlieger, Sep 22 2017 *)
PROG
(Magma) [8*n * 2^(n-1) + 1: n in [0..30]]; // Vincenzo Librandi, Sep 23 2011
(PARI) Vec((1+4*x-4*x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ Colin Barker, Feb 18 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved