A231080 - OEIS

A231080

T(n,k) = number of n X k 0..3 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, and upper left element zero.

0, 0, 0, 0, 2, 0, 0, 14, 2, 0, 0, 40, 50, 16, 0, 0, 356, 136, 784, 34, 0, 0, 1840, 2820, 6400, 5098, 154, 0, 0, 10128, 38000, 523936, 71944, 54426, 432, 0, 0, 60808, 421920, 18937480, 18655220, 1866192, 441392, 1618, 0, 0, 337016, 6118120, 696453136, 1782634608, 1480839364, 32292680, 4164402, 5058, 0

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OFFSET

1,5

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..83

FORMULA

Empirical for column k:

k=2: a(n) = 2*a(n-1) +6*a(n-2) -5*a(n-3)

k=3: [order 11]

k=4: [order 36]

Empirical for row n:

n=2: a(n) = 3*a(n-1) +12*a(n-2) +30*a(n-3) -64*a(n-4) +16*a(n-5)

n=3: [order 35]

EXAMPLE

Table starts:

0 0 0 0 0 0 0

0 2 14 40 356 1840 10128

0 2 50 136 2820 38000 421920

0 16 784 6400 523936 18937480 696453136

0 34 5098 71944 18655220 1782634608 190102522528

0 154 54426 1866192 1480839364 417868659864 131563996224512

0 432 441392 32292680 79624748768 61990953794520 ...

0 1618 4164402 679262904 5187293040908 ...

...

Some solutions for n=3 k=4:

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

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

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

CROSSREFS

Columns 2..6 are A230800, A231076, A231077, A231078, A231079.

Rows 2..5 are A231081, A231082, A231083, A231084.

Sequence in context: A061848 A193294 A231049 * A231246 A216991 A191418

Adjacent sequences: A231077 A231078 A231079 * A231081 A231082 A231083

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 03 2013

EXTENSIONS

Name corrected by Andrew Howroyd, Mar 21 2025

STATUS

approved