OFFSET
0,1
COMMENTS
This is the sequence of third terms of "second partial sums of m-th powers".
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Luciano Ancora, Demonstration of formulas
Index entries for linear recurrences with constant coefficients, signature (6,-11,6).
FORMULA
G.f.: -2*(13*x^2-13*x+3) / ((x-1)*(2*x-1)*(3*x-1)). - Colin Barker, Jan 24 2015
a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3). - Colin Barker, Jan 24 2015
MATHEMATICA
Table[2^(n+1)+3^n+3, {n, 0, 30}] (* or *) LinearRecurrence[{6, -11, 6}, {6, 10, 20}, 30] (* Harvey P. Dale, Mar 27 2025 *)
PROG
(PARI) a(n)=2<<n + 3^n + 3 \\ Charles R Greathouse IV, Jan 23 2015
(PARI) Vec(-2*(13*x^2-13*x+3)/((x-1)*(2*x-1)*(3*x-1)) + O(x^100)) \\ Colin Barker, Jan 24 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Luciano Ancora, Jan 22 2015
STATUS
approved