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A118648 a(n) is the number of binary strings of length n+3 such that there exists a subsequence of length 4 with 2 ones in it. 0
11, 25, 54, 114, 237, 486, 988, 1998, 4027, 8097, 16253, 32587, 65286, 130727, 261668, 523631, 1047669, 2095900, 4192576, 8386223, 16773924, 33549888, 67102592, 134209071, 268423507, 536854419, 1073719059, 2147452226 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

COMMENTS

a(n) = 2^(n+4) - sum of all elements of the n-th power of the matrix [[1 1 0 0 0] [0 0 1 0 0] [0 0 0 1 0] [0 0 0 0 1] [1 1 0 0 0]] which is the transition matrix for the last four bits being 0000, 0001, 0010, 0100, 1000. - Joshua Zucker, Aug 04 2006

LINKS

Table of n, a(n) for n=4..31.

Index entries for linear recurrences with constant coefficients, signature (3,-2,0,1,-2).

FORMULA

G.f. -x^4*(-11+8*x-x^2-2*x^3+8*x^4) / ( (2*x-1)*(x^4+x-1) ). - R. J. Mathar, Nov 28 2011

CROSSREFS

Sequence in context: A031025 A140675 A161532 * A262105 A105270 A039337

Adjacent sequences:  A118645 A118646 A118647 * A118649 A118650 A118651

KEYWORD

nonn

AUTHOR

Tanya Khovanova, May 10 2006

STATUS

approved

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Last modified April 28 16:04 EDT 2017. Contains 285578 sequences.