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A021029
Expansion of 1/((1-x)*(1-2*x)*(1-3*x)*(1-6*x)).
3
1, 12, 97, 672, 4333, 26964, 164809, 998184, 6017605, 36192156, 217414561, 1305276336, 7834033117, 47011340388, 282089500153, 1692601439928, 10155802087669, 60935393132460, 365614101138385
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
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
Cf. A001240 (first differences).
Sequence in context: A121791 A016753 A078605 * A270496 A128594 A166793
KEYWORD
nonn,easy
STATUS
approved