A282732 Satisfies the recurrence a(n) = 3*a(n-1)-a(n-2)+a(n-3)-2*a(n-4)+2*a(n-5).

1, 3, 9, 23, 63, 171, 461, 1247, 3371, 9111, 24629, 66575, 179959, 486451, 1314933, 3554415, 9607995, 25971519, 70204013, 189769551, 512968999, 1386614411, 3748178797, 10131759903, 27387316427, 74031077351, 200114546757, 540932717135, 1462203568951, 3952505014627, 10684077253253, 28880293973327

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Julien Leroy, Michel Rigo, and Manon Stipulanti, Behavior of Digital Sequences Through Exotic Numeration Systems, Electronic Journal of Combinatorics 24(1) (2017), #P1.44. See Section 4.

Index entries for linear recurrences with constant coefficients, signature (3,-1,1,-2,2).

Formula

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

Maple

a:=proc(n) option remember;
if n=0 then 1
elif n=1 then 3
elif n=2 then 9
elif n=3 then 23
elif n=4 then 63
else 3*a(n-1)-a(n-2)+a(n-3)-2*a(n-4)+2*a(n-5);
fi;
end;
[seq(a(n), n=0..40)];

Mathematica

LinearRecurrence[{3, -1, 1, -2, 2}, {1, 3, 9, 23, 63}, 40] (* Harvey P. Dale, Jun 06 2020 *)

Prog

(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

Crossrefs

Sequence in context: A029852 A354645 A371956 * A253244 A018044 A047045

Adjacent sequences: A282729 A282730 A282731 * A282733 A282734 A282735

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 03 2017

Status

approved