A087432 Expansion of 1+x*(1-x-4*x^2)/((1+x)*(1-2*x)*(1-3*x)).

1, 1, 3, 7, 19, 51, 143, 407, 1179, 3451, 10183, 30207, 89939, 268451, 802623, 2402407, 7196299, 21567051, 64657463, 193885007, 581480259, 1744091251, 5231574703, 15693326007, 47077181819, 141225953051, 423666674343

Offset: 0

Author

Paul Barry, Sep 02 2003

Keywords

• nonn
• easy

Comments

Binomial transform of A047849 (with interpolated zeros, 1,0,2,0,6,0,...). Binomial transform is A087433.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-1,-6).

Crossrefs

First differences of A093379.

Programs

Mathematica

CoefficientList[Series[1+x (1-x-4x^2)/((1+x)(1-2x)(1-3x)),{x,0,30}],x] (* or *) LinearRecurrence[{4,-1,-6},{1,1,3,7},30] (* Harvey P. Dale, Aug 23 2017 *)

PARI

Vec((x-1)*(2*x^2+2*x-1)/((1+x)*(1-2*x)*(1-3*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012, corrected Nov 27 2014

Formula

a(n) = (-1)^n/6+2^n/3+3^n/6, n>0.

For n>4, a(n) = 6*a(n-1) - 9*a(n-2) - 4*a(n-3) + 12*a(n-4). - Gary W. Adamson, Jun 14 2006