A021029 Expansion of 1/((1-x)*(1-2*x)*(1-3*x)*(1-6*x)).

1, 12, 97, 672, 4333, 26964, 164809, 998184, 6017605, 36192156, 217414561, 1305276336, 7834033117, 47011340388, 282089500153, 1692601439928, 10155802087669, 60935393132460, 365614101138385

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A001240 (first differences).

Programs

Magma

[(-1+5*2^(n+2)-5*3^(n+2)+6^(n+2))/10: n in [0..20]]; // Vincenzo Librandi, 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 *)

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