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A223633 Number of n X 4 0..1 arrays with rows, antidiagonals and columns unimodal. 1
11, 121, 801, 3712, 13599, 42109, 114713, 282273, 639165, 1350228, 2689169, 5091414, 9224755, 16081503, 27096217, 44293439, 70470225, 109418622, 166193601, 247432316, 361730919, 520085521, 736404249, 1028097709, 1416755525 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 4 of A223637.

LINKS

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

FORMULA

Empirical: a(n) = (1/112)*n^8 - (1/72)*n^7 + (203/360)*n^6 + (37/360)*n^5 + (41/144)*n^4 + (901/36)*n^3 - (168481/2520)*n^2 + (5693/60)*n - 45 for n>2.

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

G.f.: x*(11 + 22*x + 108*x^2 - 65*x^3 + 249*x^4 - 74*x^5 + 92*x^6 + 18*x^7 + 9*x^8 - 11*x^9 + x^10) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>11.

(End)

EXAMPLE

Some solutions for n=4:

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

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

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

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

CROSSREFS

Cf. A223637.

Sequence in context: A262468 A221964 A223640 * A223616 A223665 A068179

Adjacent sequences:  A223630 A223631 A223632 * A223634 A223635 A223636

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 24 2013

STATUS

approved

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Last modified October 21 08:57 EDT 2021. Contains 348150 sequences. (Running on oeis4.)