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 A201618 Number of n X 1 0..3 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor. 1
 0, 4, 4, 10, 16, 26, 40, 59, 84, 116, 156, 205, 264, 334, 416, 511, 620, 744, 884, 1041, 1216, 1410, 1624, 1859, 2116, 2396, 2700, 3029, 3384, 3766, 4176, 4615, 5084, 5584, 6116, 6681, 7280, 7914, 8584, 9291, 10036, 10820, 11644, 12509, 13416, 14366, 15360 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Column 1 of A201625. LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 FORMULA Empirical: a(n) = (1/6)*n^3 - n^2 + (35/6)*n - 9 for n>4. For n > 4 the above empirical a(n) is equal to C(n-1,3) + 4C(n-2,1) that is the n-th coefficient in Taylor series of ((1-x+x^2)/(1-x))^4 at x=0. - Nikita Gogin, Jul 24 2013 Conjectures from Colin Barker, May 23 2018: (Start) G.f.: x^2*(2 - 2*x + x^2)*(2 - 4*x + 4*x^2 - 2*x^3 + x^4) / (1 - x)^4. a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>8. (End) EXAMPLE Some solutions for n=10: ..1....0....0....2....1....1....1....0....0....0....0....1....2....0....0....0 ..1....0....0....2....1....1....1....0....0....0....0....1....2....0....0....0 ..1....0....2....2....1....1....1....0....0....1....1....1....3....0....1....0 ..1....1....2....2....1....2....1....0....0....1....1....2....3....0....1....0 ..2....1....3....2....1....2....1....0....1....3....1....2....3....0....2....2 ..2....2....3....2....1....2....1....0....1....3....1....2....3....3....2....2 ..2....2....3....2....1....3....2....2....1....3....1....2....3....3....3....2 ..2....2....3....2....1....3....2....2....2....3....1....2....3....3....3....2 ..2....3....3....3....2....3....3....2....2....3....1....2....3....3....3....2 ..2....3....3....3....2....3....3....2....2....3....1....2....3....3....3....2 CROSSREFS Sequence in context: A209423 A185784 A185904 * A341243 A050339 A087288 Adjacent sequences:  A201615 A201616 A201617 * A201619 A201620 A201621 KEYWORD nonn AUTHOR R. H. Hardin, Dec 03 2011 STATUS approved

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Last modified May 14 16:23 EDT 2021. Contains 343884 sequences. (Running on oeis4.)