A283323 a(n) = 4*a(n-2)+1 with initial terms 1,3,7.

1, 3, 7, 13, 29, 53, 117, 213, 469, 853, 1877, 3413, 7509, 13653, 30037, 54613, 120149, 218453, 480597, 873813, 1922389, 3495253, 7689557, 13981013, 30758229, 55924053, 123032917, 223696213, 492131669, 894784853, 1968526677, 3579139413, 7874106709, 14316557653, 31496426837, 57266230613

Offset

0,2

Links

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

A. J. Macfarlane, Generating functions for integer sequences defined by the evolution of cellular automata with even rule numbers, 2016. See Fig. 13.

Index entries for linear recurrences with constant coefficients, signature (1,4,-4).

Formula

From Colin Barker, Mar 16 2017: (Start)

G.f.: (1 + 2*x - 2*x^3) / ((1 - x)*(1 - 2*x)*(1 + 2*x)).

a(n) = (-4 + (-2)^n + 21*2^n) / 12 for n>0.

a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) for n>3.

(End)

Maple

f:=proc(n) option remember;
if n=0 then 1 elif n=1 then 3 elif n=2 then 7
else 4*f(n-2)+1; fi; end;
[seq(f(n), n=0..40)];

Mathematica

LinearRecurrence[{1, 4, -4}, {1, 3, 7, 13}, 36] (* or *) CoefficientList[Series[(1 + 2*x - 2*x^3) / ((1 - x)*(1 - 2*x)*(1 + 2*x)) , {x, 0, 35}], x] (* Indranil Ghosh, Mar 16 2017 *)

Prog

(PARI) Vec((1 + 2*x - 2*x^3) / ((1 - x)*(1 - 2*x)*(1 + 2*x)) + O(x^40)) \\ Colin Barker, Mar 16 2017

Crossrefs

Sequence in context: A283705 A284401 A284542 * A260022 A134270 A091565

Adjacent sequences: A283320 A283321 A283322 * A283324 A283325 A283326

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 16 2017

Status

approved