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 A222334 T(n,k)=Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..k array extended with zeros and convolved with 1,1 6
 2, 2, 3, 2, 3, 4, 2, 3, 4, 6, 2, 3, 4, 7, 9, 2, 3, 4, 7, 11, 13, 2, 3, 4, 7, 11, 17, 19, 2, 3, 4, 7, 11, 18, 27, 28, 2, 3, 4, 7, 11, 18, 29, 42, 41, 2, 3, 4, 7, 11, 18, 29, 46, 66, 60, 2, 3, 4, 7, 11, 18, 29, 47, 74, 104, 88, 2, 3, 4, 7, 11, 18, 29, 47, 76, 118, 163, 129, 2, 3, 4, 7, 11, 18, 29, 47 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ....2....2.....2.....2.....2.....2.....2.....2.....2.....2.....2 ....3....3.....3.....3.....3.....3.....3.....3.....3.....3.....3 ....4....4.....4.....4.....4.....4.....4.....4.....4.....4.....4 ....6....7.....7.....7.....7.....7.....7.....7.....7.....7.....7 ....9...11....11....11....11....11....11....11....11....11....11 ...13...17....18....18....18....18....18....18....18....18....18 ...19...27....29....29....29....29....29....29....29....29....29 ...28...42....46....47....47....47....47....47....47....47....47 ...41...66....74....76....76....76....76....76....76....76....76 ...60..104...118...122...123...123...123...123...123...123...123 ...88..163...189...197...199...199...199...199...199...199...199 ..129..256...303...317...321...322...322...322...322...322...322 ..189..402...485...511...519...521...521...521...521...521...521 ..277..631...777...824...838...842...843...843...843...843...843 ..406..991..1244..1328..1354..1362..1364..1364..1364..1364..1364 ..595.1556..1992..2141..2188..2202..2206..2207..2207..2207..2207 ..872.2443..3190..3451..3535..3561..3569..3571..3571..3571..3571 .1278.3836..5108..5563..5712..5759..5773..5777..5778..5778..5778 .1873.6023..8180..8967..9229..9313..9339..9347..9349..9349..9349 .2745.9457.13099.14454.14912.15061.15108.15122.15126.15127.15127 Empirical: for n<=2k+1, T(n,k)=A080023(n)=A169985(n), which is A000032(n) for n>=2. - Danny Rorabaugh, Mar 13 2015 LINKS R. H. Hardin, Table of n, a(n) for n = 1..9501 FORMULA Empirical for column k: k=1: a(n) = a(n-1)+a(n-3) k=2: a(n) = a(n-1)+a(n-3)+a(n-5) k=3: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7) k=4: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9) k=5: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)+a(n-11) k=6: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)+a(n-11)+a(n-13) k=7: a(n) = a(n-1)+a(n-3)+a(n-5)+a(n-7)+a(n-9)+a(n-11)+a(n-13)+a(n-15) EXAMPLE Some solutions for n=6 k=4, one extended zero followed by filtered positions ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0 ..0....0....1....0....1....0....1....0....1....0....0....1....0....1....0....0 ..0....0....0....1....0....0....0....1....0....0....0....0....0....0....1....1 ..0....1....1....0....0....1....0....0....1....0....0....0....1....0....0....0 ..0....0....0....0....0....0....0....0....0....1....0....0....0....1....1....0 ..0....1....0....0....1....0....0....1....1....0....1....0....0....0....0....0 ..1....0....0....1....0....1....1....0....0....0....0....0....0....0....0....0 CROSSREFS Column 1 is A000930(n+2). Column 2 is A222122. Columns 3 to 7 are A222329 to A222333. Cf. A000032, A080023, A169985. Sequence in context: A222027 A222127 A221999 * A340716 A181948 A238943 Adjacent sequences:  A222331 A222332 A222333 * A222335 A222336 A222337 KEYWORD nonn,tabl AUTHOR R. H. Hardin Feb 15 2013 STATUS approved

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Last modified June 25 04:52 EDT 2021. Contains 345452 sequences. (Running on oeis4.)