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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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 30 2014
STATUS
approved

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Last modified May 23 21:14 EDT 2024. Contains 372765 sequences. (Running on oeis4.)