A288170 a(n) = 3*a(n-1) - a(n-2) - 4*a(n-3) + 2*a(n-4) for n >= 4, where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 16, a(4) = 34, a(5) = 70 .

2, 4, 8, 16, 34, 70, 144, 292, 590, 1186, 2380, 4768, 9546, 19102, 38216, 76444, 152902, 305818, 611652, 1223320, 2446658, 4893334, 9786688, 19573396, 39146814, 78293650, 156587324, 313174672, 626349370, 1252698766, 2505397560, 5010795148, 10021590326

Offset

0,1

Comments

Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iteration of the mapping 00->0010, 1->000, starting with 00; see A288167.

Links

Clark Kimberling, Table of n, a(n) for n = 0..2000

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

Formula

a(n) = 3*a(n-1) - a(n-2) - 4*a(n-3) + 2*a(n-4) for n >= 4, where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 16, a(4) = 34, a(5) = 70 .

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

a(n) = (3 + (-1)^n + 7*2^(1+n) - 6*n) / 6 for n>0. - Colin Barker, Sep 29 2017

Mathematica

Join[{2}, LinearRecurrence[{3, -1, -3, 2}, {4, 8, 16, 34}, 40]]

Prog

(PARI) Vec(2*(1 - x - x^2 + x^3 + x^4) / ((1 - x)^2*(1 + x)*(1 - 2*x)) + O(x^30)) \\ Colin Barker, Sep 29 2017

Crossrefs

Cf. A288167.

Sequence in context: A275545 A273972 A275443 * A088325 A215930 A367660

Adjacent sequences: A288167 A288168 A288169 * A288171 A288172 A288173

Keyword

nonn,easy

Author

Clark Kimberling, Jun 07 2017

Status

approved