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

Author

Creighton Dement, Aug 14 2005

Keywords

• easy
• nonn

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

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

Crossrefs

Cf. A111665, A111666.

Programs

Mathematica

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

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