A282732 - OEIS

%I #15 Oct 29 2023 09:46:11

%S 1,3,9,23,63,171,461,1247,3371,9111,24629,66575,179959,486451,1314933,

%T 3554415,9607995,25971519,70204013,189769551,512968999,1386614411,

%U 3748178797,10131759903,27387316427,74031077351,200114546757,540932717135,1462203568951,3952505014627,10684077253253,28880293973327

%N Satisfies the recurrence a(n) = 3*a(n-1)-a(n-2)+a(n-3)-2*a(n-4)+2*a(n-5).

%H Colin Barker, <a href="/A282732/b282732.txt">Table of n, a(n) for n = 0..1000</a>

%H Julien Leroy, Michel Rigo, and Manon Stipulanti, <a href="https://doi.org/10.37236/6581">Behavior of Digital Sequences Through Exotic Numeration Systems</a>, Electronic Journal of Combinatorics 24(1) (2017), #P1.44. See Section 4.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,1,-2,2).

%F G.f.: (1 + x^2 - 2*x^3 + 2*x^4) / (1 - 3*x + x^2 - x^3 + 2*x^4 - 2*x^5). - _Colin Barker_, Mar 04 2017

%p a:=proc(n) option remember;

%p if n=0 then 1

%p elif n=1 then 3

%p elif n=2 then 9

%p elif n=3 then 23

%p elif n=4 then 63

%p else 3*a(n-1)-a(n-2)+a(n-3)-2*a(n-4)+2*a(n-5);

%p fi;

%p end;

%p [seq(a(n),n=0..40)];

%t LinearRecurrence[{3,-1,1,-2,2},{1,3,9,23,63},40] (* _Harvey P. Dale_, Jun 06 2020 *)

%o (PARI) Vec((1 + x^2 - 2*x^3 + 2*x^4) / (1 - 3*x + x^2 - x^3 + 2*x^4 - 2*x^5) + O(x^40)) \\ _Colin Barker_, Mar 04 2017

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Mar 03 2017