OFFSET
0,2
COMMENTS
a(n) is the area of the (n+3)-gon with vertices (2^k,3^k) for 0 <= k <= n+2. - J. M. Bergot and Robert Israel, Dec 05 2020
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (12,-47,72,-36).
FORMULA
G.f.: 1/((1-x)*(1-2*x)*(1-3*x)*(1-6*x)).
a(n) = (-1+5*2^(n+2)-5*3^(n+2)+6^(n+2))/10. - Bruno Berselli, Sep 02 2011
MAPLE
seq(-1/10 + 2^(n+1) - (9*3^n)/2 + (18*6^n)/5, n=0..40); # Robert Israel, Dec 05 2020
MATHEMATICA
CoefficientList[Series[1/((1 - x)(1 - 2x)(1 - 3x)(1 - 6x)), {x, 0, 30}], x] (* Harvey P. Dale, Mar 14 2011 *)
PROG
(Magma) [(-1+5*2^(n+2)-5*3^(n+2)+6^(n+2))/10: n in [0..20]]; // Vincenzo Librandi, Sep 02 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved