A285665 a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) + 2*a(n-5) - 2*a(n-7) for n>7 and where a(0)=2, a(1)=3, a(2)=6, a(3)=10, a(4)=17, a(5)=29, a(6)=51.

2, 3, 6, 10, 17, 29, 51, 90, 160, 282, 499, 881, 1559, 2758, 4880, 8634, 15275, 27025, 47815, 84598, 149680, 264826, 468555, 829009, 1466759, 2595126, 4591536, 8123770, 14373323, 25430609, 44994183, 79607862, 140849584, 249204090, 440914891, 780107345

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->001, 1->000, starting with 00; see A286939.

Links

Clark Kimberling, Table of n, a(n) for n = 0..3000

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

Formula

G.f.: (2 + x - x^2 - 3*x^5 - 2*x^6)/(1 - x - 2*x^2 + x^3 + x^4 - 2*x^5 + 2 x^7) = (2 + x - x^2 - 3*x^5 - 2*x^6)/((1 - x)*(1 + x)*(1 - x + x^2)*(1 - 2*x^2 - 2*x^3)).

Mathematica

LinearRecurrence[{1, 2, -1, -1, 2, 0, -2}, {2, 3, 6, 10, 17, 29, 51}, 40]

Crossrefs

Cf. A286939.

Sequence in context: A238777 A344615 A245437 * A135431 A123908 A233268

Adjacent sequences: A285662 A285663 A285664 * A285666 A285667 A285668

Keyword

nonn,easy

Author

Clark Kimberling, Jun 05 2017

Status

approved