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A251107 Number of (n+1) X (2+1) 0..2 arrays with no 2 X 2 subblock having the maximum of its diagonal elements greater than the absolute difference of its antidiagonal elements 1
147, 810, 3616, 15281, 67518, 304870, 1369052, 6118942, 27356256, 122402144, 547700666, 2450461705, 10963429165, 49051483677, 219461893981, 981894966609, 4393096675995, 19655164658898, 87939229945039, 393449138915943 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 2 of A251113.

LINKS

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

Robert Israel, Maple-assisted proof of empirical recurrence

FORMULA

Empirical: a(n) = 11*a(n-1) - 53*a(n-2) + 169*a(n-3) - 400*a(n-4) + 717*a(n-5) - 999*a(n-6) + 1063*a(n-7) - 860*a(n-8) + 543*a(n-9) - 268*a(n-10) + 115*a(n-11) - 40*a(n-12) + 9*a(n-13) - a(n-14).

Empirical formula verified: see link. - Robert Israel, Feb 03 2019

EXAMPLE

Some solutions for n=4:

  0 0 2   1 2 2   0 2 2   1 0 1   0 0 1   0 0 0   0 0 2

  0 0 2   0 0 2   1 0 2   1 0 1   0 0 1   2 2 2   0 0 2

  0 0 0   1 0 2   1 0 1   1 1 0   1 0 0   0 0 0   0 0 0

  2 0 0   1 0 0   2 0 0   0 1 1   1 0 0   2 2 2   1 0 0

  2 2 2   2 2 2   2 2 1   0 0 0   2 1 0   0 0 0   2 1 0

MAPLE

f:= proc(i, j)

  local Li, Lj;

  Li:= convert(i+27, base, 3)[1..3];

  Lj:= convert(j+27, base, 3)[1..3];

  if max(Li[1], Lj[2])<=abs(Li[2]-Lj[1])

    and max(Li[2], Lj[3])<=abs(Li[3]-Lj[2])

    then 1 else 0

  fi

end proc:

T:= Matrix(27, 27, f):

u:= Vector(27, 1):

Tu[0]:= u:

for n from 1 to 30 do Tu[n]:= T . Tu[n-1] od:

seq(u^%T . Tu[n], n=1..30); # Robert Israel, Feb 03 2019

CROSSREFS

Sequence in context: A162701 A063701 A261939 * A183741 A020328 A075925

Adjacent sequences:  A251104 A251105 A251106 * A251108 A251109 A251110

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 30 2014

STATUS

approved

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Last modified August 8 19:29 EDT 2020. Contains 336298 sequences. (Running on oeis4.)