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A233813 Number of (n+1) X (3+1) 0..5 arrays with every 2 X 2 subblock having the sum of the squares of all six edge and diagonal differences equal to 11. 1
1824, 10972, 61896, 403108, 2384304, 16476460, 100402408, 727727388, 4526565112, 34009964384, 214493580576, 1653020851316, 10519851847336, 82472356844020, 527892783810376, 4185126298632084, 26885993638734088, 214690431691380868 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

R. H. Hardin, Empirical recurrence of order 78

Robert Israel, Maple-assisted proof of empirical recurrence

FORMULA

Empirical recurrence of order 78 (see link above).

Empirical recurrence verified (see link). - Robert Israel, Jul 30 2019

EXAMPLE

Some solutions for n=3

..1..2..1..0....3..4..3..2....3..4..3..4....2..0..2..0....1..1..2..1

..0..0..0..2....4..2..2..4....4..2..4..2....1..0..1..0....2..3..3..3

..1..2..1..0....4..3..4..3....2..3..2..3....0..2..2..2....2..4..5..4

..2..0..2..0....2..4..2..4....1..1..1..3....1..0..1..0....2..3..5..3

MAPLE

Rows:= [seq(seq(seq(seq([w, x, y, z], z=max(y-2, 0)..min(y+2, 5)), y=max(x-2, 0)..min(x+2, 5)), x=max(w-2, 0)..min(w+2, 5)), w=0..5)]:

nrows:= nops(Rows):

filter:= proc(x) local i, j; add(add((x[i]-x[j])^2, i=j+1..4), j=1..3)=11 end proc:

T:= Matrix(nrows, nrows, proc(i, j) local k; if andmap(filter, [seq([Rows[i][k], Rows[i][k+1], Rows[j][k], Rows[j][k+1]], k=1..3)]) then 1 else 0 fi end proc):

U[0]:= Vector(nrows, 1):

for j from 1 to 30 do U[j]:= T . U[j-1] od:

seq(add(U[n][i], i=1..nrows), n=1..30); # Robert Israel, Jul 30 2019

CROSSREFS

Column 3 of A233818.

Sequence in context: A179581 A230052 A234222 * A249536 A124073 A259950

Adjacent sequences:  A233810 A233811 A233812 * A233814 A233815 A233816

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 16 2013

STATUS

approved

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Last modified March 4 02:14 EST 2021. Contains 341773 sequences. (Running on oeis4.)