A196337 -id:A196337 - cp's OEIS frontend

A196332 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,3,1,2 for x=0,1,2,3,4.

4, 8, 7, 50, 111, 259, 744, 1840, 4761, 12491, 33073, 86147, 225519, 592444, 1548876, 4064416, 10672675, 27999791, 73482986, 192857345, 506140823, 1328448433, 3487163834, 9153779129, 24028409740, 63075279907, 165574433166, 434640853456

Offset: 1

R. H. Hardin Oct 01 2011

nonn

Every 0 is next to 0 4'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 2's

Column 3 of A196337

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

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

Empirical: a(n) = 3*a(n-1) -a(n-3) -5*a(n-4) +6*a(n-5) +6*a(n-6) -22*a(n-7) -71*a(n-8) +6*a(n-9) +95*a(n-10) +3*a(n-11) +139*a(n-12) -20*a(n-13) -45*a(n-14) +44*a(n-15) -6*a(n-16) -14*a(n-17)

A196333 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,3,1,2 for x=0,1,2,3,4.

Original entry on oeis.org

5, 17, 50, 335, 894, 3246, 14973, 64423, 270901, 1067992, 4278465, 17554846, 73250696, 303360883, 1240601669, 5071382869, 20820082942, 85773230271, 353226448334, 1451624154342, 5960878160915, 24492093845487, 100710579314169

Offset: 1

R. H. Hardin Oct 01 2011

nonn

Every 0 is next to 0 4'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 2's

Column 4 of A196337

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

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

Empirical: a(n) = 5*a(n-1) -4*a(n-2) +26*a(n-4) +56*a(n-5) -358*a(n-6) -748*a(n-7) -896*a(n-8) +909*a(n-9) +187*a(n-10) -12078*a(n-11) +42445*a(n-12) +97050*a(n-13) +246286*a(n-14) +522734*a(n-15) +662122*a(n-16) -574583*a(n-17) -2576076*a(n-18) -7793975*a(n-19) -18081736*a(n-20) -11777431*a(n-21) -37101001*a(n-22) -40924777*a(n-23) +19988497*a(n-24) +20268565*a(n-25) +59783847*a(n-26) +29293979*a(n-27) +59333365*a(n-28) -2116548*a(n-29) -34111094*a(n-30) -18558798*a(n-31) -28606287*a(n-32) -8559806*a(n-33) -18722495*a(n-34) +1768049*a(n-35) +8214636*a(n-36) +12355852*a(n-37) +15376*a(n-38) +6620070*a(n-39) +393935*a(n-40) +4096014*a(n-41) -2372022*a(n-42) +503938*a(n-43) -494622*a(n-44) -65073*a(n-45) -85243*a(n-46) -185276*a(n-47) +85167*a(n-48) -25581*a(n-49) +7530*a(n-50) +4334*a(n-51) -193*a(n-52) +967*a(n-53) -255*a(n-54)

A196334 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,3,1,2 for x=0,1,2,3,4.

Original entry on oeis.org

8, 34, 111, 894, 3793, 25295, 169152, 868710, 4661189, 28620947, 176947794, 1020483285, 5753457776, 33726487544, 201541895718, 1182711274308, 6838120164129, 39848553924565, 234753917513044, 1378789238484503

Offset: 1

R. H. Hardin Oct 01 2011

nonn

Every 0 is next to 0 4'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 2's

Column 5 of A196337

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

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

A196335 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,3,1,2 for x=0,1,2,3,4.

Original entry on oeis.org

12, 62, 259, 3246, 25295, 237905, 1783508, 14742650, 131257701, 1161104389, 9477920113, 79981857183, 698216221745, 5973531188672, 50458097968498, 431717763820004, 3722514631710593, 31795825068196111, 270678277789108068

Offset: 1

R. H. Hardin Oct 01 2011

nonn

Every 0 is next to 0 4'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 2's

Column 6 of A196337

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

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

A196336 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,3,1,2 for x=0,1,2,3,4.

Original entry on oeis.org

17, 123, 744, 14973, 169152, 1783508, 20775275, 288083607, 3804352736, 45025949276, 551749790508, 6938656473356, 86871212883112, 1084929546742079, 13732256293307465, 172093176937103403, 2135921380879622460

Offset: 1

R. H. Hardin Oct 01 2011

nonn

Every 0 is next to 0 4'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 2's

Column 7 of A196337

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

R. H. Hardin, Table of n, a(n) for n = 1..127

A196331 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,0,3,1,2 for x=0,1,2,3,4.

Original entry on oeis.org

1, 5, 7, 335, 3793, 237905, 20775275, 5845172493, 2321484416437

Offset: 1

R. H. Hardin Oct 01 2011

nonn

Every 0 is next to 0 4'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 2's

Diagonal of A196337

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

cp's OEIS Frontend

A196332 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,3,1,2 for x=0,1,2,3,4.

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A196333 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,3,1,2 for x=0,1,2,3,4.

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A196334 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,3,1,2 for x=0,1,2,3,4.

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A196335 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,3,1,2 for x=0,1,2,3,4.

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A196336 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,0,3,1,2 for x=0,1,2,3,4.

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A196331 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,0,3,1,2 for x=0,1,2,3,4.

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