A305889 a(n) = 3*a(n-2) + a(n-4), a(0)=a(1)=0, a(2)=1, a(3)=2.

0, 0, 1, 2, 3, 6, 10, 20, 33, 66, 109, 218, 360, 720, 1189, 2378, 3927, 7854, 12970, 25940, 42837, 85674, 141481, 282962, 467280, 934560, 1543321, 3086642, 5097243, 10194486, 16835050, 33670100, 55602393, 111204786, 183642229, 367284458, 606529080

Offset

0,4

Comments

Difference table:

0, 0, 1, 2, 3, 6, 10, 20, 33, 66, ... = a(n)

0, 1, 1, 1, 3, 4, 10, 13, 33, 43, ... = b(n)

1, 0, 0, 2, 1, 6, 3, 20, 10, 66, ... = c(n).

c(2n+1)=a(2n+1), c(2n+2)=a(2n).

Links

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

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

Formula

a(2n) = A006190(n), a(2n+1) = 2*a(2n).

G.f.: x^2*(1 + 2*x) / (1 - 3*x^2 - x^4). - Colin Barker, Jun 14 2018

Mathematica

Nest[Append[#, 3 #[[-2]] + #[[-4]]] &, {0, 0, 1, 2}, 33] (* or *)
CoefficientList[Series[x^2*(1 + 2 x)/(1 - 3 x^2 - x^4), {x, 0, 36}], x] (* Michael De Vlieger, Jun 14 2018 *)
LinearRecurrence[{0, 3, 0, 1}, {0, 0, 1, 2}, 41] (* Robert G. Wilson v, Jul 10 2018 *)

Prog

(PARI) concat(vector(2), Vec(x^2*(1 + 2*x) / (1 - 3*x^2 - x^4) + O(x^40))) \\ Colin Barker, Jun 14 2018

Crossrefs

Cf. A006190 (bisection of a(n),b(n) and, from the second 0,c(n)).

Cf. A003688(n+1) (from the third 1, bisection of b(n)).

Sequence in context: A050291 A324739 A214002 * A135452 A077027 A030436

Adjacent sequences: A305886 A305887 A305888 * A305890 A305891 A305892

Keyword

nonn,easy

Author

Paul Curtz, Jun 14 2018

Status

approved