A111665 - OEIS

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)).

%I #22 Mar 09 2024 16:26:32

%S 1,2,3,4,5,10,23,56,141,366,955,2496,6529,17090,44739,117124,306629,

%T 802762,2101655,5502200,14404941,37712622,98732923,258486144,

%U 676725505,1771690370,4638345603,12143346436,31791693701,83231734666,217903510295

%N 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)).

%C 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[ * ]

%H Colin Barker, <a href="/A111665/b111665.txt">Table of n, a(n) for n = 0..1000</a>

%H Robert Munafo, <a href="https://mrob.com/pub/seq/floretion.html">Sequences Related to "Floretions"</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,0,1,-3,1).

%F 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

%t LinearRecurrence[{3, -1, 0, 1, -3, 1}, {1, 2, 3, 4, 5, 10}, 50] (* _Paolo Xausa_, Mar 09 2024 *)

%o (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

%Y Cf. A111664, A111666.

%K easy,nonn

%O 0,2

%A _Creighton Dement_, Aug 14 2005