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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.)