A197475 -id:A197475 - cp's OEIS frontend

A197469 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.

1, 2, 6, 12, 24, 50, 98, 194, 394, 786, 1562, 3138, 6282, 12530, 25082, 50210, 100330, 200658, 401498, 802818, 1605450, 3211442, 6422714, 12844514, 25690282, 51381138, 102759194, 205520322, 411044874, 822081650, 1644162938, 3288342434

Offset: 1

R. H. Hardin, Oct 15 2011

nonn

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

Column 2 of A197475.

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

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

Cf. A197475.

Empirical: a(n) = a(n-1) +4*a(n-3) for n>6.

Empirical g.f.: x*(1 + x + 4*x^2 + 2*x^3 + 4*x^4 + 2*x^5) / ((1 - 2*x)*(1 + x + 2*x^2)). - Colin Barker, May 12 2018

A197470 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

3, 6, 26, 46, 181, 374, 1300, 2886, 9446, 22060, 69096, 167466, 507600, 1265434, 3741192, 9529514, 27644128, 71580304, 204668940, 536641128, 1517618972, 4017418484, 11266355518, 30042504088, 83713614532, 224474050480

Offset: 1

R. H. Hardin Oct 15 2011

nonn

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

Column 3 of A197475

			Some solutions containing all values 0 to 4 for n=4
..0..1..1....2..0..2....1..2..0....2..0..2....2..0..2....2..0..2....1..1..0
..3..0..2....0..4..0....1..0..3....0..4..0....0..4..0....0..4..0....2..0..3
..0..4..0....1..0..3....0..4..0....2..0..3....3..0..2....3..0..1....0..4..0
..2..0..2....1..2..0....2..0..2....1..1..0....0..1..1....0..2..1....2..0..2

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

Empirical: a(n) = 6*a(n-2) +3*a(n-3) +4*a(n-4) -2*a(n-5) +2*a(n-6) -7*a(n-7) -19*a(n-8) -23*a(n-9) -19*a(n-10) -19*a(n-11) -4*a(n-12) -4*a(n-13) for n>16

A197471 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

1, 12, 46, 184, 748, 2824, 10934, 42474, 164782, 638460, 2473902, 9589038, 37167908, 144059050, 558354234, 2164121964, 8387927204, 32510787510, 126008566828, 488396574430, 1892976376006, 7336987712088, 28437432700816, 110220652223106

Offset: 1

R. H. Hardin Oct 15 2011

nonn

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

Column 4 of A197475

			Some solutions containing all values 0 to 4 for n=5
..2..0..3..0....1..2..0..2....0..3..0..1....0..3..0..2....0..2..0..2
..0..4..0..3....1..0..4..0....3..0..3..1....2..0..4..0....1..1..2..0
..2..0..1..0....0..1..0..3....0..4..0..2....1..1..0..2....2..0..2..1
..1..2..1..2....2..1..3..0....3..0..3..0....0..2..1..1....0..4..0..1
..1..0..2..0....0..2..0..2....0..2..1..1....2..0..2..0....2..0..3..0

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

Empirical: a(n) = a(n-1) +5*a(n-2) +19*a(n-3) +15*a(n-4) +24*a(n-5) -17*a(n-6) -55*a(n-7) -114*a(n-8) +5*a(n-9) +182*a(n-10) +372*a(n-11) +28*a(n-12) -230*a(n-13) -289*a(n-14) -284*a(n-15) -44*a(n-16) +101*a(n-17) +174*a(n-18) -28*a(n-19) +80*a(n-20) +8*a(n-21) -8*a(n-22) +144*a(n-23) -48*a(n-25) for n>28

A197472 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

4, 24, 181, 748, 5408, 22672, 151748, 684002, 4368923, 20344854, 126020110, 603916958, 3643523708, 17866994674, 105586791488, 527450827498, 3064686007756, 15542757419162, 89084044386061, 457335065118848

Offset: 1

R. H. Hardin Oct 15 2011

nonn

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

Column 5 of A197475

			Some solutions containing all values 0 to 4 for n=4
..0..2..0..2..1....0..2..1..1..0....2..0..1..1..0....1..1..2..0..2
..1..1..3..0..1....3..0..3..0..3....0..4..0..2..1....0..2..0..4..0
..0..3..0..4..0....0..4..0..3..0....3..0..1..0..1....2..1..3..0..3
..2..0..3..0..2....2..0..2..1..1....0..2..1..2..0....0..1..0..3..0

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

Empirical: a(n) = 15*a(n-2) +52*a(n-3) +296*a(n-4) -554*a(n-5) -229*a(n-6) -6613*a(n-7) -4335*a(n-8) -20874*a(n-9) +18040*a(n-10) +26381*a(n-11) +197933*a(n-12) +94070*a(n-13) +320192*a(n-14) -611325*a(n-15) -1087899*a(n-16) -3359414*a(n-17) -3589742*a(n-18) -3585120*a(n-19) +1625011*a(n-20) +12448300*a(n-21) +40979440*a(n-22) +72913510*a(n-23) +84642420*a(n-24) +58563471*a(n-25) -78408358*a(n-26) -285525148*a(n-27) -449083891*a(n-28) -430038062*a(n-29) -48315877*a(n-30) +332137526*a(n-31) +647232602*a(n-32) +895796784*a(n-33) +402347451*a(n-34) -71569578*a(n-35) -971116816*a(n-36) -915055737*a(n-37) -564795248*a(n-38) -408261834*a(n-39) +1616488905*a(n-40) +1209618295*a(n-41) +359637734*a(n-42) +1627078813*a(n-43) +458140995*a(n-44) -1790490027*a(n-45) -302830462*a(n-46) +118180618*a(n-47) -2049684292*a(n-48) -430429020*a(n-49) +1970991956*a(n-50) -371957378*a(n-51) -1143603688*a(n-52) +1515158904*a(n-53) +487108128*a(n-54) -935714152*a(n-55) +420116328*a(n-56) +641573360*a(n-57) -440594128*a(n-58) -327892352*a(n-59) +177462144*a(n-60) +7058112*a(n-61) -111894784*a(n-62) +26606336*a(n-63) +48291584*a(n-64) -3591168*a(n-65) -8124416*a(n-66) +135168*a(n-67) +61440*a(n-68) for n>71

A197473 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

4, 50, 374, 2824, 22672, 165200, 1265828, 9507212, 72145488, 544829612, 4121917612, 31166838320, 235726500646, 1782712177744, 13482608699280, 101968288116918, 771180418816752, 5832406885650952, 44110365514811080

Offset: 1

R. H. Hardin Oct 15 2011

nonn

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

Column 6 of A197475

			Some solutions containing all values 0 to 4 for n=4
..2..0..3..0..1..1....0..3..0..1..1..0....0..3..0..2..1..1....1..0..3..0..1..1
..0..3..0..4..0..2....3..0..4..0..2..1....3..0..4..0..3..0....1..3..0..4..0..2
..2..1..1..0..3..0....0..4..0..3..0..1....0..4..0..4..0..2....2..0..1..0..4..0
..0..2..0..2..1..1....2..0..1..1..2..0....2..0..3..0..1..1....0..2..1..2..0..2

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

A197474 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

5, 98, 1300, 10934, 151748, 1265828, 16544206, 145244408, 1830370547, 16537658774, 202870487557, 1878224690406, 22527034080238, 212875475502774, 2505004507267645, 24087191716817350, 278905922435987885

Offset: 1

R. H. Hardin Oct 15 2011

nonn

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

Column 7 of A197475

			Some solutions containing all values 0 to 4 for n=4
..2..0..1..1..0..3..0....1..0..3..0..2..1..1....1..1..2..0..1..2..0
..0..4..0..2..1..0..3....1..2..0..4..0..2..0....0..3..0..2..1..0..3
..1..0..4..0..1..2..0....0..2..1..0..3..1..2....3..0..3..1..0..4..0
..1..2..0..3..0..1..1....2..0..1..2..0..1..0....0..3..0..1..2..0..2

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

A197468 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.

Original entry on oeis.org

1, 2, 26, 184, 5408, 165200, 16544206, 2117012786, 779857304215, 396015611721478, 546971557228648382

Offset: 1

R. H. Hardin Oct 15 2011

nonn

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

Diagonal of A197475

			Some solutions containing all values 0 to 4 for n=4
..1..2..0..2....0..3..0..2....1..1..0..1....2..0..3..0....2..0..2..1
..1..0..4..0....2..0..4..0....2..0..3..1....0..4..0..1....0..4..0..1
..0..3..0..3....1..3..0..1....0..4..0..2....3..0..2..1....3..0..4..0
..1..1..2..0....1..0..2..1....2..0..3..0....0..1..1..0....0..3..0..2

cp's OEIS Frontend

A197469 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.

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A197470 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.

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A197471 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.

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A197472 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.

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A197473 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.

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A197474 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.

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A197468 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.

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