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 A223659 Number of n X 1 [0..3] arrays with row sums unimodal and column sums inverted unimodal. 19
 4, 16, 50, 130, 296, 610, 1163, 2083, 3544, 5776, 9076, 13820, 20476, 29618, 41941, 58277, 79612, 107104, 142102, 186166, 241088, 308914, 391967, 492871, 614576, 760384, 933976, 1139440, 1381300, 1664546, 1994665, 2377673, 2820148, 3329264 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Column 1 of A223663. Apparently also column 4 of A071920. - R. J. Mathar, May 17 2014 LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 Kyu-Hwan Lee, Se-jin Oh, Catalan triangle numbers and binomial coefficients, arXiv:1601.06685 [math.CO], 2016. FORMULA Empirical: a(n) = (1/720)*n^6 + (1/48)*n^5 + (23/144)*n^4 + (9/16)*n^3 + (241/180)*n^2 + (11/12)*n + 1 = 1 + n*(n+1)*(n^4+14*n^3+101*n^2+304*n+660)/720. Empirical G.f.: -x*(x^2-2*x+2)*(x^4-4*x^3+6*x^2-4*x+2) / (x-1)^7. - R. J. Mathar, May 14 2014 EXAMPLE Some solutions for n=3 ..2....2....0....1....1....3....1....0....3....1....2....1....2....1....0....2 ..2....2....1....3....3....3....3....2....2....2....2....3....0....1....1....1 ..2....0....2....2....0....1....3....3....1....0....3....1....0....1....1....0 CROSSREFS Cf. A071920, A223663. Sequence in context: A262268 A231156 A271483 * A217953 A217952 A217951 Adjacent sequences:  A223656 A223657 A223658 * A223660 A223661 A223662 KEYWORD nonn AUTHOR R. H. Hardin, Mar 25 2013 STATUS approved

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Last modified April 13 09:12 EDT 2021. Contains 342935 sequences. (Running on oeis4.)