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 A118430 Number of binary sequences of length n containing exactly one subsequence 010. 10
 0, 0, 0, 1, 4, 10, 22, 47, 98, 199, 396, 777, 1508, 2900, 5534, 10492, 19782, 37119, 69358, 129118, 239578, 443229, 817822, 1505389, 2764986, 5068435, 9273928, 16940488, 30897020, 56271128, 102347564, 185922589, 337353688, 611462514 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS With only two 0's at the beginning, the convolution of A005314 with itself. Column 1 of A118429. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 T. Mansour, M. Shattuck, Counting Peaks and Valleys in a Partition of a Set , J. Int. Seq. 13 (2010), 10.6.8, Lemma 2.1, k=2, 1 peak. Index entries for linear recurrences with constant coefficients, signature (4,-6,6,-5,2,-1). FORMULA G.f.: z^3/(1-2*z+z^2-z^3)^2. EXAMPLE a(4) = 4 because we have 0100, 0101, 0010 and 1010. MAPLE g:=z^3/(1-2*z+z^2-z^3)^2: gser:=series(g, z=0, 40): seq(coeff(gser, z, n), n=0..38); MATHEMATICA LinearRecurrence[{4, -6, 6, -5, 2, -1}, {0, 0, 0, 1, 4, 10}, 40] (* Jean-François Alcover, May 11 2019 *) CROSSREFS Cf. A005314, A118429, A255386. Sequence in context: A266374 A008267 A056112 * A178452 A324536 A137247 Adjacent sequences:  A118427 A118428 A118429 * A118431 A118432 A118433 KEYWORD nonn AUTHOR Emeric Deutsch, Apr 27 2006 STATUS approved

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Last modified December 6 08:53 EST 2019. Contains 329788 sequences. (Running on oeis4.)