A223282 -id:A223282 - cp's OEIS frontend

A223277 Rolling icosahedron face footprints: number of n X 3 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

9, 87, 849, 8295, 81057, 792087, 7740273, 75637959, 739134273, 7222821495, 70581425169, 689721818919, 6739962906081, 65862930139863, 643612676665521, 6289384281642375, 61459874978079873, 600586013379170103

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Column 3 of A223282.

			Some solutions for n=3:
..0..2..3....0..2..3....0..1..4....0..5..9....0..1..6....0..2..0....0..5..9
..0..2..3....8..2..3....0..1..4....0..5..0....0..1..0....3..2..8....9..5..9
..0..2..8....0..2..8....0..1..4....0..1..0....4..1..4....3..2..8....0..5..7
Face neighbors:
0 -> 1 2 5
1 -> 0 4 6
2 -> 0 3 8
3 -> 2 4 16
4 -> 3 1 17
5 -> 0 7 9
6 -> 1 7 10
7 -> 6 5 11
8 -> 2 9 13
9 -> 8 5 14
10 -> 6 12 17
11 -> 7 12 14
12 -> 11 10 19
13 -> 8 15 16
14 -> 9 11 15
15 -> 14 13 19
16 -> 3 13 18
17 -> 4 10 18
18 -> 16 17 19
19 -> 15 18 12

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

Cf. A223282.

Empirical: a(n) = 11*a(n-1) - 12*a(n-2).
Conjectures from Colin Barker, Aug 18 2018: (Start)
G.f.: 3*x*(3 - 4*x) / (1 - 11*x + 12*x^2).
a(n) = (2^(-1-n)*((11-sqrt(73))^n*(-7+sqrt(73)) + (7+sqrt(73))*(11+sqrt(73))^n)) / sqrt(73).
(End)

A223278 Rolling icosahedron face footprints: number of n X 4 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

Original entry on oeis.org

27, 351, 4995, 72279, 1048923, 15229647, 221142771, 3211159815, 46628577099, 677084057343, 9831800199267, 142765577323191, 2073070007320635, 30102629340815919, 437114178530327763, 6347246378746198887

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Column 4 of A223282.

			Some solutions for n=3:
..0..2..3.16....0..2..0..1....0..1..0..1....0..2..0..1....0..5..0..1
..8..2..3..2....0..5..0..1....4..1..4..1....0..1..0..5....0..2..0..1
..3..2..3.16....7..5..0..5....4..1..6..1....4..1..0..5....3..2..0..5
Face neighbors:
0 -> 1 2 5
1 -> 0 4 6
2 -> 0 3 8
3 -> 2 4 16
4 -> 3 1 17
5 -> 0 7 9
6 -> 1 7 10
7 -> 6 5 11
8 -> 2 9 13
9 -> 8 5 14
10 -> 6 12 17
11 -> 7 12 14
12 -> 11 10 19
13 -> 8 15 16
14 -> 9 11 15
15 -> 14 13 19
16 -> 3 13 18
17 -> 4 10 18
18 -> 16 17 19
19 -> 15 18 12

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

Cf. A223282.

Empirical: a(n) = 17*a(n-1) - 36*a(n-2).
Conjectures from Colin Barker, Aug 18 2018: (Start)
G.f.: 27*x*(1 - 4*x) / (1 - 17*x + 36*x^2).
a(n) = (3*2^(-1-n)*((17-sqrt(145))^n*(-1+sqrt(145)) + (1+sqrt(145))*(17+sqrt(145))^n)) / sqrt(145).
(End)

A223279 Rolling icosahedron face footprints: number of n X 5 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

Original entry on oeis.org

81, 1575, 38457, 1024071, 28271577, 792881031, 22392745881, 634400697159, 17998034165721, 510923724667143, 14507984391789081, 412013548109024967, 11701449873880124505, 332336795068373382279, 9438910778776181239449

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Column 5 of A223282.

			Some solutions for n=3:
  0 1 0 1 4     0 1 0 5 9     0 5 0 2 0     0 1 4 1 6
  6 1 0 1 0     0 5 0 5 7     0 5 0 2 8     4 1 4 1 4
  0 1 0 1 6     9 5 0 5 9     9 5 0 2 3     6 1 6 1 6
Face neighbors:
   0 ->  1  2  5
   1 ->  0  4  6
   2 ->  0  3  8
   3 ->  2  4 16
   4 ->  3  1 17
   5 ->  0  7  9
   6 ->  1  7 10
   7 ->  6  5 11
   8 ->  2  9 13
   9 ->  8  5 14
  10 ->  6 12 17
  11 ->  7 12 14
  12 -> 11 10 19
  13 ->  8 15 16
  14 ->  9 11 15
  15 -> 14 13 19
  16 ->  3 13 18
  17 ->  4 10 18
  18 -> 16 17 19
  19 -> 15 18 12

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

Cf. A223282.

Empirical: a(n) = 45*a(n-1) - 518*a(n-2) + 1268*a(n-3) + 1704*a(n-4) - 4064*a(n-5) + 1536*a(n-6).

Empirical g.f.: 3*x*(9 - 68*x + 64*x^2)*(3 - 54*x - 76*x^2 + 56*x^3) / (1 - 45*x + 518*x^2 - 1268*x^3 - 1704*x^4 + 4064*x^5 - 1536*x^6). - Colin Barker, Aug 18 2018

A223280 Rolling icosahedron face footprints: number of nX6 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

Original entry on oeis.org

243, 6831, 261819, 10979127, 473368227, 20570223999, 895927195659, 39047604482055, 1702160040384051, 74204651599582287, 3234961829070975771, 141029297731894387287, 6148230806876335875267, 268034791871130540563487

Offset: 1

R. H. Hardin Mar 19 2013

nonn

Column 6 of A223282

			Some solutions for n=3
..0..2..3..2..3..2....0..5..0..1..0..1....0..5..0..5..0..5....0..2..0..1..4..1
..0..2..8..2..8..2....0..5..0..2..0..2....0..5..0..2..0..1....0..2..0..1..0..1
..8..2..0..2..8.13....0..5..0..2..3..2....7..5..0..2..0..5....0..1..0..1..6..1
Face neighbors:
0 -> 1 2 5
1 -> 0 4 6
2 -> 0 3 8
3 -> 2 4 16
4 -> 3 1 17
5 -> 0 7 9
6 -> 1 7 10
7 -> 6 5 11
8 -> 2 9 13
9 -> 8 5 14
10 -> 6 12 17
11 -> 7 12 14
12 -> 11 10 19
13 -> 8 15 16
14 -> 9 11 15
15 -> 14 13 19
16 -> 3 13 18
17 -> 4 10 18
18 -> 16 17 19
19 -> 15 18 12

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

Empirical: a(n) = 63*a(n-1) -882*a(n-2) +792*a(n-3) +35736*a(n-4) -70768*a(n-5) -246208*a(n-6) +327936*a(n-7) +146432*a(n-8) -180224*a(n-9)

A223281 Rolling icosahedron face footprints: number of nX7 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

Original entry on oeis.org

729, 29943, 1881441, 137621799, 10801441521, 879050854455, 72981761306721, 6127190749734087, 517631500569076305, 43882777288012073559, 3727442176083442555713, 316954431035692378210023

Offset: 1

R. H. Hardin Mar 19 2013

nonn

Column 7 of A223282

			Some solutions for n=3
..0..1..0..2..3..4..3....0..1..0..2..8..2..0....0..1..4..3.16..3.16
..0..1..0..2..3..4.17....0..5..0..2..0..2..3....0..1..4..3..2..3..2
..0..1..0..2..3..4..1....0..5..0..2..8..2..8....0..1..4..3..2..8..2
Face neighbors:
0 -> 1 2 5
1 -> 0 4 6
2 -> 0 3 8
3 -> 2 4 16
4 -> 3 1 17
5 -> 0 7 9
6 -> 1 7 10
7 -> 6 5 11
8 -> 2 9 13
9 -> 8 5 14
10 -> 6 12 17
11 -> 7 12 14
12 -> 11 10 19
13 -> 8 15 16
14 -> 9 11 15
15 -> 14 13 19
16 -> 3 13 18
17 -> 4 10 18
18 -> 16 17 19
19 -> 15 18 12

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

Empirical: a(n) = 193*a(n-1) -13138*a(n-2) +389164*a(n-3) -4361048*a(n-4) -16478976*a(n-5) +680367552*a(n-6) -2205737728*a(n-7) -32395676672*a(n-8) +159364997888*a(n-9) +669407522304*a(n-10) -3582601411584*a(n-11) -5951537518592*a(n-12) +34040410587136*a(n-13) +16838602686464*a(n-14) -137580342149120*a(n-15) +18193951227904*a(n-16) +210744868077568*a(n-17) -92999396622336*a(n-18) -80015240724480*a(n-19) +37572373905408*a(n-20)

A223283 Rolling icosahedron face footprints: number of 2 X n 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

Original entry on oeis.org

20, 15, 87, 351, 1575, 6831, 29943, 130815, 572103, 2501199, 10936215, 47815839, 209064807, 914089455, 3996657207, 17474508351, 76403468295, 334057454991, 1460593174743, 6386124254175, 27921931810983, 122082540957999

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Row 2 of A223282.

			Some solutions for n=3:
  0 1 4   0 1 4   0 5 0   0 1 6   0 1 0   0 5 7   0 1 6
  4 1 0   4 1 4   7 5 7   0 1 4   0 5 0   9 5 0   4 1 0
Face neighbors:
   0 ->  1  2  5
   1 ->  0  4  6
   2 ->  0  3  8
   3 ->  2  4 16
   4 ->  3  1 17
   5 ->  0  7  9
   6 ->  1  7 10
   7 ->  6  5 11
   8 ->  2  9 13
   9 ->  8  5 14
  10 ->  6 12 17
  11 ->  7 12 14
  12 -> 11 10 19
  13 ->  8 15 16
  14 ->  9 11 15
  15 -> 14 13 19
  16 ->  3 13 18
  17 ->  4 10 18
  18 -> 16 17 19
  19 -> 15 18 12

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

Cf. A223282.

Empirical: a(n) = 3*a(n-1) + 6*a(n-2) for n>3.

Empirical g.f.: x*(20 - 45*x - 78*x^2) / (1 - 3*x - 6*x^2). - Colin Barker, Aug 18 2018

A223284 Rolling icosahedron face footprints: number of 3 X n 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

Original entry on oeis.org

400, 75, 849, 4995, 38457, 261819, 1881441, 13196979, 93567177, 660226923, 4668616305, 32981553891, 233097416793, 1647108262683, 11639737522305, 82252298336787, 581246168781033, 4107418513432011, 29025468445135761

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Row 3 of A223282.

			Some solutions for n=3:
  0 2 3   0 1 0   0 5 7   0 5 9   0 1 0   0 1 6   0 5 9
  8 2 3   6 1 4   9 5 9   0 5 9   4 1 6   0 1 4   9 5 9
  8 2 3   6 1 0   7 5 9   0 5 9   6 1 4   4 1 0   7 5 9
Face neighbors:
   0 ->  1  2  5
   1 ->  0  4  6
   2 ->  0  3  8
   3 ->  2  4 16
   4 ->  3  1 17
   5 ->  0  7  9
   6 ->  1  7 10
   7 ->  6  5 11
   8 ->  2  9 13
   9 ->  8  5 14
  10 ->  6 12 17
  11 ->  7 12 14
  12 -> 11 10 19
  13 ->  8 15 16
  14 ->  9 11 15
  15 -> 14 13 19
  16 ->  3 13 18
  17 ->  4 10 18
  18 -> 16 17 19
  19 -> 15 18 12

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

Cf. A223282.

Empirical: a(n) = 5*a(n-1) + 18*a(n-2) - 24*a(n-3) for n>4.

Empirical g.f.: x*(400 - 1925*x - 6726*x^2 + 9000*x^3) / (1 - 5*x - 18*x^2 + 24*x^3). - Colin Barker, Aug 18 2018

A223285 Rolling icosahedron face footprints: number of 4 X n 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

Original entry on oeis.org

8000, 375, 8295, 72279, 1024071, 10979127, 137621799, 1576368663, 19009505799, 222545715447, 2650002132711, 31248496329687, 370552575553479, 4379948164268727, 51867287743753383, 613557282050858391

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Row 4 of A223282.

			Some solutions for n=3:
  0 1 0   0 2 0   0 2 8   0 5 7   0 1 4   0 2 3   0 1 4
  4 1 4   0 2 8   8 2 3   9 5 9   4 1 0   8 2 0   6 1 6
  6 1 4   0 2 3   0 2 8   9 5 0   0 1 6   0 2 8   6 1 6
  6 1 0   8 2 8   3 2 0   9 5 0   6 1 6   0 2 8   4 1 0
Face neighbors:
   0 ->  1  2  5
   1 ->  0  4  6
   2 ->  0  3  8
   3 ->  2  4 16
   4 ->  3  1 17
   5 ->  0  7  9
   6 ->  1  7 10
   7 ->  6  5 11
   8 ->  2  9 13
   9 ->  8  5 14
  10 ->  6 12 17
  11 ->  7 12 14
  12 -> 11 10 19
  13 ->  8 15 16
  14 ->  9 11 15
  15 -> 14 13 19
  16 ->  3 13 18
  17 ->  4 10 18
  18 -> 16 17 19
  19 -> 15 18 12

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

Cf. A223282.

Empirical: a(n) = 5*a(n-1) + 92*a(n-2) - 56*a(n-3) - 920*a(n-4) + 192*a(n-5) + 1152*a(n-6) for n>7.

Empirical g.f.: x*(8000 - 39625*x - 729580*x^2 + 444304*x^3 + 7280536*x^4 - 1517376*x^5 - 9097344*x^6) / (1 - 5*x - 92*x^2 + 56*x^3 + 920*x^4 - 192*x^5 - 1152*x^6). - Colin Barker, Aug 18 2018

A223286 Rolling icosahedron face footprints: number of 5Xn 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

Original entry on oeis.org

160000, 1875, 81057, 1048923, 28271577, 473368227, 10801441521, 200475062187, 4265203621833, 82829709506163, 1709099202398433, 33866115603026427, 689396112362771001, 13783610690189186115, 278907343566603743697

Offset: 1

R. H. Hardin Mar 19 2013

nonn

Row 5 of A223282

			Some solutions for n=3
..0..1..4....0..2..0....0..2..8....0..5..9....0..5..0....0..2..3....0..1..6
..4..1..0....0..5..0....0..2..0....0..5..0....0..1..0....0..2..8....4..1..4
..6..1..6....9..5..9....3..2..0....0..1..0....6..1..0....8..2..3....4..1..6
..6..7..6....9..8..9....8..2..3....4..1..0....0..1..4....3..2..3....6..1..4
.11..7.11...13..8..2....8..2..3....0..1..6....4..1..6....3..4..3....6..1..4
Face neighbors:
0 -> 1 2 5
1 -> 0 4 6
2 -> 0 3 8
3 -> 2 4 16
4 -> 3 1 17
5 -> 0 7 9
6 -> 1 7 10
7 -> 6 5 11
8 -> 2 9 13
9 -> 8 5 14
10 -> 6 12 17
11 -> 7 12 14
12 -> 11 10 19
13 -> 8 15 16
14 -> 9 11 15
15 -> 14 13 19
16 -> 3 13 18
17 -> 4 10 18
18 -> 16 17 19
19 -> 15 18 12

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

Empirical: a(n) = 13*a(n-1) +278*a(n-2) -2372*a(n-3) -11584*a(n-4) +98256*a(n-5) +68096*a(n-6) -1208064*a(n-7) +753664*a(n-8) +4509696*a(n-9) -4485120*a(n-10) -4571136*a(n-11) +4718592*a(n-12) for n>13

A223287 Rolling icosahedron face footprints: number of 6 X n 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

Original entry on oeis.org

3200000, 9375, 792087, 15229647, 792881031, 20570223999, 879050854455, 26073158735535, 1008694505830119, 32094483162308319, 1178050642133703831, 38926413103761206799, 1389205962179205980487, 46849778740107421135935

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Row 6 of A223282.

			Some solutions for n=3
..0..5..0....0..5..0....0..5..0....0..5..0....0..5..0....0..5..0....0..5..0
..0..5..9....7..5..9....0..5..0....7..5..9....9..5..9....0..5..9....9..5..7
..7..5..0....7..5..7....9..5..9....0..5..7....7..5..0....7..5..0....9..5..7
..0..5..9....0..5..9....9..5..9....9..5..9....9..5..0....9..5..9....7..5..0
..9..5..0....7..5..0....9..8..9....9..5..0....7..5..0....9.14..9....7..5..7
..9..5..9....0..5..9...13..8..2....7..5..9....7..5..7...11.14..9....7..5..0
Face neighbors:
0 -> 1 2 5
1 -> 0 4 6
2 -> 0 3 8
3 -> 2 4 16
4 -> 3 1 17
5 -> 0 7 9
6 -> 1 7 10
7 -> 6 5 11
8 -> 2 9 13
9 -> 8 5 14
10 -> 6 12 17
11 -> 7 12 14
12 -> 11 10 19
13 -> 8 15 16
14 -> 9 11 15
15 -> 14 13 19
16 -> 3 13 18
17 -> 4 10 18
18 -> 16 17 19
19 -> 15 18 12

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

Cf. A223282.

Empirical: a(n) = 13*a(n-1) +1244*a(n-2) -8256*a(n-3) -402464*a(n-4) +1780288*a(n-5) +55907168*a(n-6) -197740288*a(n-7) -4040907520*a(n-8) +12437493760*a(n-9) +166070886400*a(n-10) -452922138624*a(n-11) -4093663121408*a(n-12) +9761715879936*a(n-13) +62363887337472*a(n-14) -126220206735360*a(n-15) -595038449696768*a(n-16) +978337484767232*a(n-17) +3542610027216896*a(n-18) -4455273209004032*a(n-19) -12803732509032448*a(n-20) +11344509988241408*a(n-21) +26381276122447872*a(n-22) -14571020149063680*a(n-23) -27374953313599488*a(n-24) +7085252929388544*a(n-25) +10449758510383104*a(n-26) for n>27.

cp's OEIS Frontend

A223277 Rolling icosahedron face footprints: number of n X 3 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

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A223278 Rolling icosahedron face footprints: number of n X 4 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

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A223279 Rolling icosahedron face footprints: number of n X 5 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

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A223280 Rolling icosahedron face footprints: number of nX6 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

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A223281 Rolling icosahedron face footprints: number of nX7 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

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A223283 Rolling icosahedron face footprints: number of 2 X n 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

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A223284 Rolling icosahedron face footprints: number of 3 X n 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

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A223285 Rolling icosahedron face footprints: number of 4 X n 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

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A223286 Rolling icosahedron face footprints: number of 5Xn 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.

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A223287 Rolling icosahedron face footprints: number of 6 X n 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.