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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
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
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
MATHEMATICA
LinearRecurrence[{3, -2, 0, 1, -2}, {11, 25, 54, 114, 237}, 30] (* Harvey P. Dale, Aug 14 2019 *)
CROSSREFS
Sequence in context: A140675 A161532 A328560 * A262105 A105270 A039337
KEYWORD
nonn
AUTHOR
Tanya Khovanova, May 10 2006
STATUS
approved