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A287381 a(n) = a(n-1) + 2*a(n-2) - a(n-3), where a(0) = 2, a(1) = 4, a(2) = 7. 3
2, 4, 7, 13, 23, 42, 75, 136, 244, 441, 793, 1431, 2576, 4645, 8366, 15080, 27167, 48961, 88215, 158970, 286439, 516164, 930072, 1675961, 3019941, 5441791, 9805712, 17669353, 31838986, 57371980, 103380599, 186285573, 335674791, 604865338, 1089929347 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Conjecture:  a(n) is the number of letters (0s and 1s) in the n-th iteration of the mapping 00->0010, 1->10, starting with 00; see A287931.

LINKS

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

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

FORMULA

a(n) = a(n-1) + 2*a(n-2) - a(n-3), where a(0) = 2, a(1) = 4, a(2) = 7.

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

MATHEMATICA

LinearRecurrence[{1, 2, -1}, {2, 4, 7}, 40]

CROSSREFS

Cf. A287931, A078038 (signed version).

Sequence in context: A303666 A260917 A165648 * A078038 A190502 A048888

Adjacent sequences:  A287378 A287379 A287380 * A287382 A287383 A287384

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 07 2017

STATUS

approved

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Last modified November 22 03:43 EST 2019. Contains 329388 sequences. (Running on oeis4.)