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A066067 Number of binary strings u of any length with property that length(u) + number of 0's in u <= n (only one of a string and its reversal are counted). 2
1, 2, 3, 6, 10, 18, 29, 49, 78, 128, 203, 329, 523, 844, 1347, 2172, 3480, 5614, 9023, 14567, 23466, 37910, 61165, 98865, 159677, 258190, 417283, 674890, 1091214, 1765146, 2854793, 4618373, 7470614, 12086436, 19552903, 31635193, 51181367, 82809832 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If 0 is replaced by 2 (as in A007931) "length + 0-bits" is simply the total of ternary digits (e.g., 3 for 21 instead of 01).

LINKS

Table of n, a(n) for n=1..38.

Index entries for linear recurrences with constant coefficients, signature (3,-1,-4,4,-2,1,1,-1)

FORMULA

G.f.: x(-x^7-x^4+3x^3-2x^2-x+1)/[(1-x-x^2)(1-x^2-x^4)(1-x)^2].

EXAMPLE

a(3) = 3: 0 01 111 (e.g. 01: length 2 + 1 zero = 3).

a(4) = 6: 0 01 00 011 101 1111.

a(5) =10: 0 01 00 011 101 001 010 0111 1011 11111.

MATHEMATICA

CoefficientList[Series[x (-x^7-x^4+3x^3-2x^2-x+1)/((1-x-x^2) (1-x^2-x^4) (1-x)^2), {x, 0, 50}], x] (* Harvey P. Dale, Jun 15 2011 *)

CROSSREFS

If reversals are counted as distinct then we obtain A000126.

A007931 (binary strings represented by ternary numbers),

Cf. A035615 (binary "same game").

Sequence in context: A208479 A065441 A075531 * A121364 A215006 A172516

Adjacent sequences:  A066064 A066065 A066066 * A066068 A066069 A066070

KEYWORD

nonn

AUTHOR

Frank Ellermann, Dec 02 2001

EXTENSIONS

More terms from Harvey P. Dale, Jun 15 2011

STATUS

approved

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Last modified May 14 13:50 EDT 2021. Contains 343884 sequences. (Running on oeis4.)