A111666 Expansion of (-2+3*x+3*x^2+4*x^3+3*x^4-5*x^5)/((x-1)*(x+1)*(1+x^2)*(x^2-3*x+1)).

2, 3, 4, 5, 10, 27, 68, 173, 450, 1179, 3084, 8069, 21122, 55299, 144772, 379013, 992266, 2597787, 6801092, 17805485, 46615362, 122040603, 319506444, 836478725, 2189929730, 5733310467, 15010001668, 39296694533, 102880081930

Offset: 0

Author

Creighton Dement, Aug 14 2005

Keywords

• easy
• nonn

Comments

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-1,0,1,-3,1).

Crossrefs

Cf. A111664, A111665.

Programs

Mathematica

CoefficientList[Series[(-2+3x+3x^2+4x^3+3x^4-5x^5)/((x-1)(x+1)(1+x^2)(x^2-3x+1)),{x,0,30}],x] (* or *) LinearRecurrence[{3,-1,0,1,-3,1},{2,3,4,5,10,27},30] (* Harvey P. Dale, Jan 24 2015 *)

Formula

a(0)=2, a(1)=3, a(2)=4, a(3)=5, a(4)=10, a(5)=27, a(n)=3*a(n-1)-a(n-2)+ a(n-4)- 3*a(n-5)+a(n-6). - Harvey P. Dale, Jan 24 2015