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 A200841 Number of 0..n arrays x(0..5) of 6 elements without any two consecutive increases or two consecutive decreases. 1
 64, 529, 2356, 7587, 19930, 45465, 93472, 177381, 315844, 533929, 864436, 1349335, 2041326, 3005521, 4321248, 6083977, 8407368, 11425441, 15294868, 20197387, 26342338, 33969321, 43350976, 54795885, 68651596, 85307769, 105199444 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Row 4 of A200838. LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 FORMULA Empirical: a(n) = (61/360)*n^6 + (93/40)*n^5 + (779/72)*n^4 + (521/24)*n^3 + (1801/90)*n^2 + (239/30)*n + 1. Conjectures from Colin Barker, Oct 14 2017: (Start) G.f.: x*(64 + 81*x - 3*x^2 - 36*x^3 + 22*x^4 - 7*x^5 + x^6) / (1 - x)^7. a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7. (End) EXAMPLE Some solutions for n=3 ..3....0....3....3....1....2....1....1....3....3....3....1....2....0....3....1 ..3....3....3....3....0....3....3....1....1....0....0....0....3....3....3....1 ..3....0....1....3....3....3....2....0....2....0....3....1....0....2....0....1 ..3....2....1....1....0....0....3....0....1....3....2....1....0....3....0....3 ..0....0....1....1....0....0....3....0....1....3....3....0....3....1....0....3 ..3....3....0....3....3....3....0....0....0....2....1....0....1....1....0....2 CROSSREFS Sequence in context: A066430 A115740 A100415 * A247929 A070054 A265636 Adjacent sequences:  A200838 A200839 A200840 * A200842 A200843 A200844 KEYWORD nonn AUTHOR R. H. Hardin Nov 23 2011 STATUS approved

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Last modified May 13 23:41 EDT 2021. Contains 343868 sequences. (Running on oeis4.)