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A223772 Number of n X 3 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing. 1
7, 28, 78, 180, 371, 707, 1269, 2170, 3563, 5650, 8692, 13020, 19047, 27281, 38339, 52962, 72031, 96584, 127834, 167188, 216267, 276927, 351281, 441722, 550947, 681982, 838208, 1023388, 1241695, 1497741, 1796607, 2143874, 2545655, 3008628 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 3 of A223777.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = (1/720)*n^6 + (1/80)*n^5 + (29/144)*n^4 + (25/48)*n^3 + (1727/360)*n^2 - (8/15)*n + 2.

Conjectures from Colin Barker, Aug 23 2018: (Start)

G.f.: x*(7 - 21*x + 29*x^2 - 23*x^3 + 14*x^4 - 7*x^5 + 2*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:

..0..1..1....1..0..0....1..1..1....1..0..0....1..0..0....0..0..0....0..1..0

..1..1..0....1..0..0....1..1..1....1..0..0....1..0..0....0..1..0....1..1..0

..1..0..0....0..0..0....1..1..1....1..1..0....1..1..1....1..1..1....1..0..0

CROSSREFS

Cf. A223777.

Sequence in context: A341986 A341067 A061968 * A024012 A163705 A162595

Adjacent sequences:  A223769 A223770 A223771 * A223773 A223774 A223775

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 27 2013

STATUS

approved

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Last modified May 7 02:20 EDT 2021. Contains 343636 sequences. (Running on oeis4.)