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A289131 a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 2*a(n-4) + 2*a(n-5) for n >= 6, a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 11, a(4) = 18, a(5) = 28. 2
2, 4, 7, 11, 18, 28, 43, 65, 96, 142, 205, 299, 426, 616, 871, 1253, 1764, 2530, 3553, 5087, 7134, 10204, 14299, 20441, 28632, 40918, 57301, 81875, 114642, 163792, 229327, 327629, 458700, 655306, 917449, 1310663, 1834950, 2621380, 3669955, 5242817, 7339968 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Conjecture:  a(n) is the number of letters (0's and 1's) in the n-th iterate of the mapping 00->0010, 01->011, 10->010, starting with 00; see A289128.

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..10000

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

FORMULA

a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 2*a(n-4) + 2*a(n-5) for n >= 6, a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 11, a(4) = 18, a(5) = 28.

From Colin Barker, Jul 02 2017: (Start)

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

a(n) = -(3*n)/2 + 7*2^(n/2) - 4 for n>0 and even.

a(n) = (-3*n + 5*2^((n + 3)/2) - 9) / 2 for n odd.

(End)

MATHEMATICA

Join[{2}, LinearRecurrence[{1, 3, -3, -2, 2}, {4, 7, 11, 18, 28}, 40]]

PROG

(PARI) Vec((2 + 2*x - 3*x^2 - 2*x^3 + 2*x^4 + 2*x^5) / ((1 - x)^2*(1 + x)*(1 - 2*x^2)) + O(x^50)) \\ Colin Barker, Jul 02 2017

CROSSREFS

Cf. A289128.

Sequence in context: A003403 A261666 A034412 * A054352 A091838 A288219

Adjacent sequences:  A289128 A289129 A289130 * A289132 A289133 A289134

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 28 2017

STATUS

approved

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Last modified November 28 13:18 EST 2020. Contains 338724 sequences. (Running on oeis4.)