A109786 Expansion of -(x+2*x^2+3*x^3-1+5*x^4)/((x+1)*(x^2-3*x+1)*(1+x^2)).

1, 1, 1, 1, 1, 5, 13, 33, 85, 225, 589, 1541, 4033, 10561, 27649, 72385, 189505, 496133, 1298893, 3400545, 8902741, 23307681, 61020301, 159753221, 418239361, 1094964865, 2866655233, 7505000833, 19648347265, 51440040965, 134671775629

Offset

0,6

Comments

Floretion Algebra Multiplication Program, FAMP Code: 4jbaseksumseq[ + .25'i + .25i' + .25'ii' + .25'jj' + .25'kk' + .25'jk' + .25'kj' + .25e], sumtype: Y[15],inty[ * ]

Links

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (2,1,1,2,-1).

Formula

a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=1, a(n)=2*a(n-1)+a(n-2)+a(n-3)+ 2*a(n-4)- a(n-5). - Harvey P. Dale, Apr 14 2015

Mathematica

CoefficientList[Series[-(x+2x^2+3x^3-1+5x^4)/((x+1)(x^2-3x+1)(1+x^2)), {x, 0, 30}], x] (* Harvey P. Dale, Apr 14 2015 *)
(* Alternative: *)
LinearRecurrence[{2, 1, 1, 2, -1}, {1, 1, 1, 1, 1}, 40] (* Harvey P. Dale, Apr 14 2015 *)

Crossrefs

Cf. A111665, A111666.

Sequence in context: A185454 A278764 A027051 * A283959 A055426 A146621

Adjacent sequences: A109783 A109784 A109785 * A109787 A109788 A109789

Keyword

easy,nonn

Author

Creighton Dement, Aug 14 2005

Status

approved