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A223615 Number of n X 3 0..1 arrays with rows and columns unimodal. 1
7, 49, 240, 876, 2582, 6504, 14547, 29659, 56161, 100123, 169786, 276030, 432888, 658106, 973749, 1406853, 1990123, 2762677, 3770836, 5068960, 6720330, 8798076, 11386151, 14580351, 18489381, 23235967, 28958014, 35809810, 43963276, 53609262 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 3 of A223620.

LINKS

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

FORMULA

Empirical: a(n) = (23/360)*n^6 + (31/120)*n^5 + (8/9)*n^4 + (31/24)*n^3 + (737/360)*n^2 + (29/20)*n + 1.

Conjectures from Colin Barker, Aug 21 2018: (Start)

G.f.: x*(7 + 44*x^2 - 20*x^3 + 20*x^4 - 6*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=4:

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

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

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

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

CROSSREFS

Cf. A223620.

Sequence in context: A181479 A223842 A212693 * A188768 A188757 A223947

Adjacent sequences:  A223612 A223613 A223614 * A223616 A223617 A223618

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 24 2013

STATUS

approved

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Last modified January 29 01:36 EST 2020. Contains 331328 sequences. (Running on oeis4.)