A196287 -id:A196287 - cp's OEIS frontend

A196282 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,3,1,4 for x=0,1,2,3,4.

4, 8, 7, 50, 111, 259, 728, 1800, 4696, 12185, 32136, 83679, 217955, 570882, 1489582, 3896818, 10200627, 26688308, 69841985, 182768771, 478336792, 1251948660, 3276977630, 8577766977, 22452853682, 58772743019, 153844929073, 402711226676

Offset: 1

R. H. Hardin, Sep 30 2011

nonn

Every 0 is next to 0 2's, every 1 is next to 1 0's, every 2 is next to 2 3's, every 3 is next to 3 1's, every 4 is next to 4 4's.

Column 3 of A196287.

			Some solutions for n=4
..1..1..0....0..0..1....0..0..1....0..0..0....1..0..0....1..1..1....1..0..0
..0..1..1....1..1..1....1..3..1....1..3..1....1..0..0....0..0..0....1..1..1
..0..1..1....1..3..0....1..1..0....1..1..3....1..0..0....0..0..0....0..1..1
..1..1..0....0..1..1....0..1..1....0..0..1....1..0..0....0..0..0....1..1..0

R. H. Hardin, Table of n, a(n) for n = 1..200

Cf. A196287.

Empirical: a(n) = 3*a(n-1) -a(n-3) -5*a(n-4) +6*a(n-5) +2*a(n-6) -14*a(n-7) -63*a(n-8) -7*a(n-9) +88*a(n-10) +28*a(n-11) +122*a(n-12) -20*a(n-13) -48*a(n-14).

A196283 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,3,1,4 for x=0,1,2,3,4.

Original entry on oeis.org

5, 17, 50, 335, 882, 2998, 13533, 57281, 234589, 894628, 3478771, 13926862, 56524150, 227694275, 905576485, 3600687113, 14386585452, 57666400761, 231012630142, 923586956312, 3690101366699, 14752678317193, 59020611073703

Offset: 1

R. H. Hardin Sep 30 2011

nonn

Every 0 is next to 0 2's, every 1 is next to 1 0's, every 2 is next to 2 3's, every 3 is next to 3 1's, every 4 is next to 4 4's

Column 4 of A196287

			Some solutions for n=5
..1..0..1..1....1..3..1..0....0..1..1..0....1..1..0..0....1..1..0..1
..1..3..1..0....0..1..3..0....0..1..1..0....0..1..1..1....0..1..3..1
..0..1..1..0....0..3..1..0....0..1..3..1....1..3..3..1....0..1..1..0
..0..1..3..0....0..1..1..1....0..1..3..1....1..1..1..0....1..1..1..1
..0..1..1..0....1..1..0..1....1..3..1..0....0..0..1..1....1..0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n) = 5*a(n-1) -4*a(n-2) -2*a(n-3) +29*a(n-4) +44*a(n-5) -353*a(n-6) -513*a(n-7) -564*a(n-8) -404*a(n-9) -28*a(n-10) -7593*a(n-11) +32939*a(n-12) +92755*a(n-13) +177932*a(n-14) +364932*a(n-15) +661674*a(n-16) -124416*a(n-17) -2070255*a(n-18) -6293067*a(n-19) -15286543*a(n-20) -12728809*a(n-21) -20872271*a(n-22) -26587548*a(n-23) +11637631*a(n-24) +10476672*a(n-25) +2138237*a(n-26) -1529115*a(n-27) -3134481*a(n-28) -1326559*a(n-29) +5371940*a(n-30) +1569922*a(n-31) +214244*a(n-32) +279752*a(n-33) -533526*a(n-34) -150688*a(n-35) -65558*a(n-36) -44908*a(n-37) -8124*a(n-38) -2360*a(n-39) -720*a(n-40)

A196284 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,3,1,4 for x=0,1,2,3,4.

Original entry on oeis.org

8, 34, 111, 882, 3621, 22971, 138924, 684002, 3547662, 21119073, 123417309, 672321817, 3625436742, 20487480586, 116748710539, 650239402498, 3588244785640, 20046900212152, 112856868883812, 631362977595367

Offset: 1

R. H. Hardin Sep 30 2011

nonn

Every 0 is next to 0 2's, every 1 is next to 1 0's, every 2 is next to 2 3's, every 3 is next to 3 1's, every 4 is next to 4 4's

Column 5 of A196287

			Some solutions for n=4
..0..0..0..0..1....1..1..0..0..1....1..0..1..1..0....0..0..0..0..1
..1..1..1..1..3....0..3..1..1..3....1..1..3..3..1....1..1..3..1..1
..3..1..3..3..1....1..1..1..3..1....0..1..1..1..1....1..1..1..3..0
..1..0..1..1..0....1..0..0..0..0....1..1..0..0..0....0..0..0..1..1

R. H. Hardin, Table of n, a(n) for n = 1..200

A196285 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,3,1,4 for x=0,1,2,3,4.

Original entry on oeis.org

12, 62, 259, 2998, 22971, 193137, 1306488, 10441374, 87352550, 710287441, 5397422494, 42850420911, 348219126761, 2770605337166, 21906712624064, 175575058788514, 1413026462375021, 11258561165769824, 89622355955131307

Offset: 1

R. H. Hardin Sep 30 2011

nonn

Every 0 is next to 0 2's, every 1 is next to 1 0's, every 2 is next to 2 3's, every 3 is next to 3 1's, every 4 is next to 4 4's

Column 6 of A196287

			Some solutions for n=4
..1..1..0..0..0..0....1..0..0..0..1..1....0..0..1..3..1..1....1..0..0..0..0..1
..0..1..1..3..1..1....3..1..1..1..3..0....0..0..1..1..0..0....1..3..1..1..1..3
..0..1..3..1..3..1....1..3..3..1..1..0....0..0..1..3..0..0....0..1..1..1..3..1
..1..1..0..0..0..0....0..1..1..0..1..1....0..0..1..1..0..0....1..1..0..0..0..0

R. H. Hardin, Table of n, a(n) for n = 1..200

A196286 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,3,1,4 for x=0,1,2,3,4.

Original entry on oeis.org

17, 123, 728, 13533, 138924, 1306488, 13307143, 182868341, 2172296568, 23151489546, 259759374474, 2973891043730, 33893925587254, 389550320415853, 4527825351283814, 51569682047646201, 583253931896374775

Offset: 1

R. H. Hardin Sep 30 2011

nonn

Every 0 is next to 0 2's, every 1 is next to 1 0's, every 2 is next to 2 3's, every 3 is next to 3 1's, every 4 is next to 4 4's

Column 7 of A196287

			Some solutions for n=4
..1..3..1..0..1..1..0....0..0..1..1..3..1..0....1..3..1..0..0..0..0
..0..1..1..0..1..3..1....1..1..1..0..1..1..0....0..1..3..1..1..1..1
..1..3..1..3..1..0..1....1..1..1..0..3..1..1....1..1..2..3..1..1..3
..1..0..0..1..1..0..1....0..0..1..1..1..0..1....1..0..1..1..0..0..1

R. H. Hardin, Table of n, a(n) for n = 1..180

A196281 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 2,0,3,1,4 for x=0,1,2,3,4.

Original entry on oeis.org

1, 5, 7, 335, 3621, 193137, 13307143, 3369153109, 1022753961763, 921078606743691

Offset: 1

R. H. Hardin Sep 30 2011

nonn

Every 0 is next to 0 2's, every 1 is next to 1 0's, every 2 is next to 2 3's, every 3 is next to 3 1's, every 4 is next to 4 4's

Diagonal of A196287

			Some solutions for n=4
..1..3..1..0....1..3..1..0....0..0..1..1....0..0..1..1....1..0..1..1
..0..1..3..0....0..1..1..0....1..3..1..0....1..1..1..0....3..1..1..0
..1..1..1..1....0..3..1..0....1..1..1..1....3..1..3..1....1..1..1..1
..1..0..0..1....0..1..1..0....0..0..0..1....1..0..0..1....0..0..0..1

cp's OEIS Frontend

A196282 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,3,1,4 for x=0,1,2,3,4.

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A196283 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,3,1,4 for x=0,1,2,3,4.

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A196284 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,3,1,4 for x=0,1,2,3,4.

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A196285 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,3,1,4 for x=0,1,2,3,4.

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A196286 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,3,1,4 for x=0,1,2,3,4.

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A196281 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 2,0,3,1,4 for x=0,1,2,3,4.

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