A287185 a(n) = 3*a(n-2) + a(n-3) + a(n-5) - 3*a(n-6) - a(n-7), where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 14, a(4) = 25, a(5) = 47, a(6) = 88, a(7) = 166.

2, 4, 7, 14, 25, 47, 88, 166, 311, 586, 1097, 2068, 3877, 7301, 13699, 25778, 48397, 91033, 170969, 321496, 603938, 1135456, 2133310, 4010306, 7535386, 14164226, 26616463, 50028064, 94013615, 176700655, 332068907, 624115579, 1172907376, 2204415644

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->00, starting with 00; see A288106.

Links

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

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

Formula

a(n) = 3*a(n-2) + a(n-3) + a(n-5) - 3*a(n-6) - a(n-7), where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 14, a(4) = 25, a(5) = 47, a(6) = 88, a(7) = 166.

G.f.: (2 + 4*x + x^2 - 4*x^5 - 5*x^6 - x^7)/(1 - 3*x^2 - x^3 - x^5 + 3*x^7 + x^8).

Mathematica

LinearRecurrence[{0, 3, 1, 0, 1, 0, -3, -1}, {2, 4, 7, 14, 25, 47, 88, 166}, 40]

Crossrefs

Cf. A288106.

Sequence in context: A347760 A218576 A054169 * A065491 A072810 A167606

Adjacent sequences: A287182 A287183 A287184 * A287186 A287187 A287188

Keyword

nonn,easy

Author

Clark Kimberling, Jun 06 2017

Status

approved