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A208901 Number of bitstrings of length n (with at least two runs) where the last two runs have different lengths. 5
0, 0, 4, 8, 24, 48, 112, 224, 480, 960, 1984, 3968, 8064, 16128, 32512, 65024, 130560, 261120, 523264, 1046528, 2095104, 4190208, 8384512, 16769024, 33546240, 67092480, 134201344, 268402688, 536838144, 1073676288, 2147418112, 4294836224, 8589803520 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A run is a maximal subsequence of (possibly just one) identical bits.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Aruna Gabhe, Problem 11623, Am. Math. Monthly 119 (2012) 161.

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

FORMULA

a(n) = 2^n - 2^(floor(n/2)+1).

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

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

EXAMPLE

If n=3 the bitstrings (with at least two runs) where the last runs have different lengths are 100,011,110,001 so a(3) = 4.

MATHEMATICA

Table[2^n - 2^(Floor[ n/2] + 1) ,  {n, 1, 40}]

LinearRecurrence[{2, 2, -4}, {0, 0, 4}, 40]

CROSSREFS

Cf. A056453, A208900, A208902, A208903.

Sequence in context: A180002 A266821 A306484 * A319721 A115641 A153334

Adjacent sequences:  A208898 A208899 A208900 * A208902 A208903 A208904

KEYWORD

nonn,easy

AUTHOR

David Nacin, Mar 03 2012

STATUS

approved

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)