login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A223766 Number of n X 4 0..1 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing 1
11, 56, 155, 361, 782, 1601, 3141, 5907, 10678, 18618, 31422, 51505, 82243, 128276, 195884, 293448, 432009, 625939, 893739, 1258980, 1751404, 2408203, 3275495, 4410017, 5881056, 7772640, 10186012, 13242411, 17086185, 21888262, 27850006 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 4 of A223770.

LINKS

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

FORMULA

Empirical: a(n) = (1/40320)*n^8 - (1/10080)*n^7 + (3/320)*n^6 + (1/45)*n^5 + (1109/1920)*n^4 - (4837/1440)*n^3 + (422483/10080)*n^2 - (109337/840)*n + 226 for n>4.

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

G.f.: x*(11 - 43*x + 47*x^2 + 58*x^3 - 205*x^4 + 209*x^5 - 42*x^6 - 150*x^7 + 256*x^8 - 245*x^9 + 151*x^10 - 55*x^11 + 9*x^12) / (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>13.

(End)

EXAMPLE

Some solutions for n=3:

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

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

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

CROSSREFS

Cf. A223770.

Sequence in context: A099532 A041226 A042503 * A265151 A275643 A223773

Adjacent sequences:  A223763 A223764 A223765 * A223767 A223768 A223769

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 27 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 03:32 EDT 2020. Contains 333105 sequences. (Running on oeis4.)