A020726 Expansion of 1/((1-6*x)*(1-10*x)*(1-11*x)).

1, 27, 493, 7599, 106645, 1411431, 17955757, 222093423, 2690508229, 32080473975, 377794514461, 4405195463487, 50953884924853, 585473143132359, 6690087028209805, 76090252032830991, 861988540696279717

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (27,-236,660).

Formula

a(n) = 21*a(n-1) - 110*a(n-2) + 6^n for n>1, a(0)=1, a(1)=27. - Vincenzo Librandi, Mar 11 2011

a(n) = (4*11^(n+2) - 5*10^(n+2) + 6^(n+2))/20. - Yahia Kahloune, Jun 30 2013

In general, for the expansion of 1/((1-r*x)(1-s*x)(1-t*x)) with t > s > r, we have the formula: a(n) = ((s-r)*t^(n+2) - (t-r)*s^(n+2) + (t-s)*r^(n+2))/((s-r)*(t-r)*(t-s)). - Yahia Kahloune, Sep 09 2013

a(0) = 1, a(1) = 27, a(2) = 493, a(n) = 27*a(n-1) - 236*a(n-2) + 660*a(n-3). - Harvey P. Dale, Oct 01 2014

Mathematica

CoefficientList[Series[1/((1-6x)(1-10x)(1-11x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{27, -236, 660}, {1, 27, 493}, 30] (* Harvey P. Dale, Oct 01 2014 *)

Prog

(PARI) Vec(1/((1-6*x)*(1-10*x)*(1-11*x)) + O(x^30)) \\ Jinyuan Wang, Mar 10 2020

Crossrefs

Sequence in context: A023946 A020971 A023772 * A020969 A025956 A020724

Adjacent sequences: A020723 A020724 A020725 * A020727 A020728 A020729

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved