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!)
A251160 Number of (n+1)X(1+1) 0..3 arrays with no 2X2 subblock having the maximum of its diagonal elements greater than the absolute difference of its antidiagonal elements 1
96, 552, 2658, 12001, 55131, 257417, 1201970, 5597648, 26056421, 121329295, 565030902, 2631278472, 12253239453, 57060424477, 265717806149, 1237389994220, 5762253389058, 26833543568447, 124957900541999, 581901431575301 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 1 of A251167

LINKS

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

Robert Israel, Maple-assisted proof of empirical formula

FORMULA

Empirical: a(n) = 7*a(n-1) -18*a(n-2) +43*a(n-3) -59*a(n-4) +70*a(n-5) -62*a(n-6) +33*a(n-7) -14*a(n-8) -3*a(n-9) +6*a(n-10) -a(n-11) for n>13.

Verified by Robert Israel, Jan 11 2019 (See link).

EXAMPLE

Some solutions for n=4

..0..2....2..3....1..2....3..3....1..3....0..3....1..3....1..1....0..3....0..3

..0..0....0..3....0..2....0..2....0..3....0..3....1..2....0..1....1..1....0..0

..3..0....0..3....0..1....0..0....1..1....0..3....1..1....1..0....0..0....2..2

..3..3....3..0....0..1....2..2....0..0....0..1....0..0....1..0....1..1....0..1

..0..1....3..1....1..0....0..0....3..1....0..0....1..0....3..2....0..1....3..1

MAPLE

q:= proc(a, b) local a1, a2, b1, b2;

  a1:= (a-1) mod 4; a2:= (a-1-a1)/4;

  b1:= (b-1) mod 4; b2:= (b-1-b1)/4;

  if max(b1, a2) > abs(b2-a1) then 0 else 1 fi

end proc:

T:= Matrix(16, 16, q):

u:= Vector(16, 1):

seq(u^%T . T^n . u, n=1..30); # Robert Israel, Jan 11 2019

CROSSREFS

Cf. A251167.

Sequence in context: A216372 A183684 A251167 * A233029 A216106 A268795

Adjacent sequences:  A251157 A251158 A251159 * A251161 A251162 A251163

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 30 2014

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 August 12 17:17 EDT 2020. Contains 336439 sequences. (Running on oeis4.)