A288465 a(n) = 2*a(n-1) - a(n-4), where a(0) = 2, a(1) = 4, a(2) = 6, a(3) = 10.

2, 4, 6, 10, 18, 32, 58, 106, 194, 356, 654, 1202, 2210, 4064, 7474, 13746, 25282, 46500, 85526, 157306, 289330, 532160, 978794, 1800282, 3311234, 6090308, 11201822, 20603362, 37895490, 69700672, 128199522, 235795682, 433695874, 797691076, 1467182630

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->0101, 1->10, starting with 00; see A288462.

Links

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

Index entries for linear recurrences with constant coefficients, signature (2, 0, 0, -1).

Formula

a(n) = 2*a(n-1) - a(n-4), where a(0) = 2, a(1) = 4, a(2) = 6. a(3) = 10.

G.f.: -((2*(-1 + x^2 + x^3))/(1 - 2*x + x^4)).

Mathematica

LinearRecurrence[{2, 0, 0, -1}, {2, 4, 6, 10}, 40]
CoefficientList[Series[-((2(-1+x^2+x^3))/(1-2x+x^4)), {x, 0, 40}], x] (* Harvey P. Dale, Oct 14 2021 *)

Crossrefs

Cf. A288462.

Sequence in context: A102477 A232582 A018074 * A000067 A133140 A349592

Adjacent sequences: A288462 A288463 A288464 * A288466 A288467 A288468

Keyword

nonn,easy

Author

Clark Kimberling, Jun 11 2017

Status

approved