A093379 Expansion of x(1-2x-2x^2)/((1+x)(1-2x)(1-3x)).

0, 1, 2, 5, 12, 31, 82, 225, 632, 1811, 5262, 15445, 45652, 135591, 404042, 1206665, 3609072, 10805371, 32372422, 97029885, 290914892, 872395151, 2616486402, 7848061105, 23541387112, 70618568931, 211844521982, 635511196325

Offset

0,3

Comments

Binomial transform is A085280, with leading zero.

Links

Table of n, a(n) for n=0..27.

Index entries for linear recurrences with constant coefficients, signature (4,-1,-6).

Formula

a(n)=3^n/12-(-1)^n/12+2^n/3-0^n/3;

a(n)=4a(n-1)-a(n-2)-6a(n-3).

a(n)=A015518(n)/3+A000079(n)/3-0^n/3.

Mathematica

CoefficientList[Series[x (1-2x-2x^2)/((1+x)(1-2x)(1-3x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{4, -1, -6}, {0, 1, 2, 5}, 40] (* Harvey P. Dale, May 10 2019 *)

Crossrefs

Cf. A087432.

Sequence in context: A077556 A076906 A097893 * A271929 A071359 A160999

Adjacent sequences: A093376 A093377 A093378 * A093380 A093381 A093382

Keyword

easy,nonn

Author

Paul Barry, Apr 28 2004

Status

approved