A109787 Expansion of -(1-x-2*x^2+11*x^4-3*x^3) / ((x-1)*(x+1)*(x^2-3*x+1)*(1+x^2)).

1, 2, 3, 4, 21, 58, 151, 392, 1037, 2718, 7115, 18624, 48769, 127682, 334275, 875140, 2291157, 5998330, 15703831, 41113160, 107635661, 281793822, 737745803, 1931443584, 5056584961, 13238311298, 34658348931, 90736735492, 237551857557

Offset: 0

Author

Creighton Dement, Aug 14 2005

Keywords

• easy
• nonn

Comments

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

Links

• Colin Barker, 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, A111666.

Programs

Mathematica

CoefficientList[Series[-(1-x-2x^2+11x^4-3x^3)/((x-1)(x+1)(x^2-3x+1)(1+x^2)),{x,0,40}],x] (* or *) LinearRecurrence[{3,-1,0,1,-3,1},{1,2,3,4,21,58},40] (* Harvey P. Dale, Jan 11 2020 *)

PARI

Vec((1 - x - 2*x^2 - 3*x^3 + 11*x^4) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)*(1 + x^2)) + O(x^30)) \\ Colin Barker, May 16 2019

Formula

a(n) = 3*a(n-1) - a(n-2) + a(n-4) - 3*a(n-5) + a(n-6) for n>5. - Colin Barker, May 16 2019