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A263330 Number of (n+2)X(1+2) 0..2 arrays with each row and column divisible by 11, read as a base-3 number with top and left being the most significant digits. 1
1, 1, 3, 9, 23, 51, 133, 399, 1321, 4129, 12457, 38059, 114177, 349017, 1056893, 3188001, 9592717, 28778151, 86390521, 259279771, 778196971, 2334819901, 7004459703, 21010336329, 63026931713, 189077563341, 567218511883 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Column 1 of A263333.

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) = 3*a(n-1) +16*a(n-5) -48*a(n-6) -505*a(n-10) +1515*a(n-11) -5105*a(n-15) +15315*a(n-16) -10114*a(n-20) +30342*a(n-21) +15709*a(n-25) -47127*a(n-26).

Empirical formula confirmed: see link. - Robert Israel, Jun 26 2019

EXAMPLE

Some solutions for n=4

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

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

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

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

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

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

MAPLE

States:= [seq(seq(seq([x, y, z], z=0..10), y=0..10), x=0..10)]:

T:= Matrix(1331, 1331, storage=sparse):

for i from 1 to 1331 do

   for y in [[0, 0, 0], [1, 0, 2], [2, 1, 1]] do

     z:= 3*States[i]+y mod 11;

     j:= 121*z[1]+11*z[2]+z[3] + 1;

     T[i, j]:= 1;

od od:

U[0]:= Vector([1, 0$1330]):

for j from 1 to 40 do U[j]:= T . U[j-1] od:

seq(U[n+2][1], n=1..38); # Robert Israel, Jun 26 2019

CROSSREFS

Cf. A263333.

Sequence in context: A227259 A064551 A005783 * A146440 A244331 A183155

Adjacent sequences:  A263327 A263328 A263329 * A263331 A263332 A263333

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 15 2015

STATUS

approved

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Last modified February 20 11:01 EST 2020. Contains 332073 sequences. (Running on oeis4.)