A111665 Expansion of (-1+x+2*x^2+5*x^4+3*x^3) / ((x-1)*(x+1)*(x^2-3*x+1)*(1+x^2)).

1, 2, 3, 4, 5, 10, 23, 56, 141, 366, 955, 2496, 6529, 17090, 44739, 117124, 306629, 802762, 2101655, 5502200, 14404941, 37712622, 98732923, 258486144, 676725505, 1771690370, 4638345603, 12143346436, 31791693701, 83231734666, 217903510295

Offset

0,2

Comments

Floretion Algebra Multiplication Program, FAMP Code: 4ibaseisumseq[ + .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

Robert Munafo, Sequences Related to "Floretions"

Index entries for linear recurrences with constant coefficients, signature (3,-1,0,1,-3,1).

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 13 2019

Mathematica

LinearRecurrence[{3, -1, 0, 1, -3, 1}, {1, 2, 3, 4, 5, 10}, 50] (* Paolo Xausa, Mar 09 2024 *)

Prog

(PARI) Vec((1 - x - 2*x^2 - 3*x^3 - 5*x^4) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)*(1 + x^2)) + O(x^35)) \\ Colin Barker, May 13 2019

Crossrefs

Cf. A111664, A111666.

Sequence in context: A190912 A306108 A282033 * A111666 A080475 A364133

Adjacent sequences: A111662 A111663 A111664 * A111666 A111667 A111668

Keyword

easy,nonn

Author

Creighton Dement, Aug 14 2005

Status

approved