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A223681 Number of 3 X n 0..1 arrays with rows and antidiagonals unimodal. 1
8, 64, 316, 1118, 3177, 7745, 16857, 33615, 62518, 109838, 184042, 296260, 460799, 695703, 1023359, 1471149, 2072148, 2865868, 3899048, 5226490, 6911941, 9029021, 11662197, 14907803, 18875106, 23687418, 29483254, 36417536, 44662843, 54410707 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 3 of A223680.

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 + (17/9)*n^4 + (23/24)*n^3 + (917/360)*n^2 + (77/60)*n + 1.

Conjectures from Colin Barker, Aug 22 2018: (Start)

G.f.: x*(8 + 8*x + 36*x^2 - 30*x^3 + 27*x^4 - 4*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=3:

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

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

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

CROSSREFS

Cf. A223680.

Sequence in context: A189690 A188741 A188993 * A189065 A189190 A188875

Adjacent sequences:  A223678 A223679 A223680 * A223682 A223683 A223684

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 25 2013

STATUS

approved

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Last modified January 19 14:34 EST 2022. Contains 350466 sequences. (Running on oeis4.)