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A055395 Number of bracketings of 0#0#0#...#0 giving result 0, where 0#0 = 0#1 = 1#0 = 1, 1#1 = 0. 5
1, 0, 0, 1, 4, 12, 36, 116, 392, 1350, 4696, 16500, 58572, 209824, 757440, 2752185, 10057636, 36943044, 136319052, 505086728, 1878395920, 7009239644, 26235435248, 98475145476, 370584275964, 1397918543552, 5284861554816 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Operation # can be interpreted as NOT AND. The ratio a(n)/A000108(n-1) converges to (2-sqrt(2))/2. Thanks to Soren Galatius Smith

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..500

FORMULA

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

G.f.: (1 + 2*C(x) - sqrt(1 + 4*C(x)^2))/2, where C(x) = (1 - sqrt(1 - 4*x))/2 is the g.f. of the Catalan numbers (A000108). - Paul D. Hanna, Jun 10 2016

G.f. A(x) satisfies: A(x) = x + (A(x) - C(x))^2, where C(x) = x + C(x)^2 is a g.f. of the Catalan numbers (A000108). - Paul D. Hanna, Jun 11 2016

MATHEMATICA

f[x_] := (1 - Sqrt[1 - 4*x])/2; CoefficientList[Series[(1 + 2*f[x] - Sqrt[1 + 4*(f[x])^2])/(2*x), {x, 0, 50}], x] (* G. C. Greubel, Jun 10 2016 *)

CROSSREFS

Cf. A055113, A055392, A273958.

Sequence in context: A290905 A000781 A192205 * A113990 A231179 A192010

Adjacent sequences:  A055392 A055393 A055394 * A055396 A055397 A055398

KEYWORD

nonn

AUTHOR

Jeppe Stig Nielsen, Jun 24 2000

STATUS

approved

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Last modified October 19 20:05 EDT 2018. Contains 316378 sequences. (Running on oeis4.)