A223480 -id:A223480 - cp's OEIS frontend

A223477 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 or antidiagonal neighbor moves across an icosahedral edge.

81, 3375, 147825, 6526575, 288507825, 12755926575, 563999907825, 24937217326575, 1102598111307825, 48751338478726575, 2155538829022707825, 95307078736540126575, 4213999366856734107825, 186321844088731401526575

Offset: 1

R. H. Hardin, Mar 20 2013

nonn

Column 5 of A223480.

			Some solutions for n=3:
..0..1..6.10.17....0..1..6..7..5....0..2..0..2..0....0..2..0..1..6
..6.10.17.10.12....6..7.11..7..6....8..2..0..5..7....0..1..0..1..4
.17.10.12.11.12....6..7..5..7..5....0..5..7.11.14....0..5..0..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. A223480.

Empirical: a(n) = 51*a(n-1) - 300*a(n-2).

Empirical g.f.: 27*x*(3 - 28*x) / (1 - 51*x + 300*x^2). - Colin Barker, Aug 20 2018

A223478 Rolling icosahedron face footprints: number of n X 6 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves across an icosahedral edge.

Original entry on oeis.org

243, 16875, 1296675, 101331675, 7939566675, 622332801675, 48783753036675, 3824122400271675, 299770559674506675, 23498831496975741675, 1842059141815703976675, 144397899075877259211675

Offset: 1

R. H. Hardin, Mar 20 2013

nonn

Column 6 of A223480.

			Some solutions for n=3:
..0..1..6..1..4..3....0..1..4..1..4..1....0..1..0..5..9..8....0..1..0..2..3.16
..0..1..0..1..4..1....0..1..4..1..4..3....0..5..9..5..9..5....0..2..0..2..3.16
..0..1..4..1..6..1....6..1..4..3..2..0....0..5..9.14..9.14....0..2..3..4..3..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

Cf. A223480.

Empirical: a(n) = 101*a(n-1) -1900*a(n-2) +10000*a(n-3).

Empirical g.f.: 27*x*(9 - 284*x + 2000*x^2) / (1 - 101*x + 1900*x^2 - 10000*x^3). - Colin Barker, Aug 20 2018

A223479 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 or antidiagonal neighbor moves across an icosahedral edge.

Original entry on oeis.org

729, 84375, 11374425, 1588785975, 223894186425, 31621425535575, 4468456626780825, 631526586023769975, 89256484380983132025, 12615117535169199386775, 1782968370270784918644825

Offset: 1

R. H. Hardin Mar 20 2013

nonn

Column 7 of A223480

			Some solutions for n=3
..0..5..0..5..7.11..7....0..5..0..1..4..1..6....0..5..0..5..0..2..0
..0..5..0..5..7..5..9....0..5..0..1..6..1..0....0..5..0..1..0..2..8
..0..5..9..5..9..5..7....0..1..0..1..0..5..0....0..1..4..1..0..2..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

Empirical: a(n) = 227*a(n-1) -14764*a(n-2) +411840*a(n-3) -5347200*a(n-4) +29600000*a(n-5) -48000000*a(n-6)

A223481 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 or antidiagonal neighbor moves across an icosahedral edge.

Original entry on oeis.org

400, 243, 2025, 16875, 147825, 1296675, 11374425, 99776475, 875239425, 7677601875, 67347938025, 590776238475, 5182290270225, 45459059955075, 398766959055225, 3497984511586875, 30684326686171425, 269162971152369075

Offset: 1

R. H. Hardin, Mar 20 2013

nonn

Row 3 of A223480.

			Some solutions for n=3:
..0..2..3....0..1..0....0..2..8....0..5..0....0..1..0....0..2..0....0..1..6
..3..4..1....0..2..8....3..2..8....0..5..9....0..2..0....3..2..3....6..1..6
..1..4..1....8..2..8....8..9..5....9..8..2....3..2..8....3..4..1....6.10.12
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. A223480.

Empirical: a(n) = 9*a(n-1) - 2*a(n-2) for n>4.

Empirical g.f.: x*(400 - 3357*x + 638*x^2 - 864*x^3) / (1 - 9*x + 2*x^2). - Colin Barker, Aug 20 2018

A223482 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 or antidiagonal neighbor moves across an icosahedral edge.

Original entry on oeis.org

8000, 2187, 30375, 421875, 6526575, 101331675, 1588785975, 24919035075, 390919514175, 6132664672875, 96208422848775, 1509305488830675, 23677794878309775, 371454275512532475, 5827328087571285975

Offset: 1

R. H. Hardin, Mar 20 2013

nonn

Row 4 of A223480.

			Some solutions for n=3:
..0..2..3....0..5..9....0..2..8....0..5..9....0..1..6....0..2..3....0..1..4
..0..2..8....7..5..7....3..2..8....9..5..7....6.10..6....8..2..0....0..1..6
..8..2..0....7..6..1....0..2..8....7..6..7....6..7..6....0..1..6....6..7.11
..8..2..8....7..6..7....8..2..8....7..5..9....6.10.12....6..1..0....6..7..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. A223480.

Empirical: a(n) = 17*a(n-1) - 16*a(n-2) - 76*a(n-3) + 64*a(n-4) for n>7.

Empirical g.f.: x*(8000 - 133813*x + 121196*x^2 + 548492*x^3 - 505088*x^4 - 701568*x^5 + 691200*x^6) / ((1 + 2*x)*(1 - 19*x + 54*x^2 - 32*x^3)). - Colin Barker, Aug 20 2018

A223483 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 or antidiagonal neighbor moves across an icosahedral edge.

Original entry on oeis.org

160000, 19683, 455625, 10546875, 288507825, 7939566675, 223894186425, 6318290752875, 178826926010625, 5061686863486275, 143298073856716425, 4056837300096090075, 114852424247153593425, 3251568434305627847475

Offset: 1

R. H. Hardin Mar 20 2013

nonn

Row 5 of A223480

			Some solutions for n=3
..0..5..0....0..5..0....0..5..0....0..5..0....0..5..7....0..5..0....0..5..7
..7..5..7....0..1..4....9..5..0....0..2..0....0..5..7....0..5..0....7..6..7
..9..5..9....4.17..4....0..2..8....0..2..8....7..5..9....0..5..7....7..5..9
..9..8.13....4.17..4....3..2..8....8..2..3....7..5..0....7..6..1....7..5..7
..2..8..2...18.17..4....8.13..8....0..2..3....0..1..0....1..0..2....7..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) = 33*a(n-1) -86*a(n-2) -1564*a(n-3) +7040*a(n-4) -6480*a(n-5) -5088*a(n-6) +5824*a(n-7) -512*a(n-8) for n>13

A223484 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 or antidiagonal neighbor moves across an icosahedral edge.

Original entry on oeis.org

3200000, 177147, 6834375, 263671875, 12755926575, 622332801675, 31621425535575, 1608341612382675, 82456836767805375, 4227484231555443675, 217015136003889260775, 11140133589863412595875, 571949483621302897613775

Offset: 1

R. H. Hardin Mar 20 2013

nonn

Row 6 of A223480.

			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..1..0....0..1..0....0..1..0....0..1..4....0..1..4....0..1..0....0..1..4
..0..1..4....6..1..0....6..1..4....4.17..4....4..1..4....4..1..6....0..1..4
..4..1..0....0..5..9....4..1..0...10.17.10....4.17.18....0..1..4....0..1..0
..0..1..4....9..5..0....4..1..6....4.17.10...18.16.18....4.17.10....0..1..4
..0..1..4....0..2..3....6..7..5....4.17.10...18.17..4...10.12.10....4..3.16
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. A223480.

Empirical: a(n) = 65*a(n-1) -392*a(n-2) -21060*a(n-3) +271696*a(n-4) -61920*a(n-5) -12301824*a(n-6) +41001664*a(n-7) +141738752*a(n-8) -796132352*a(n-9) -244873216*a(n-10) +5515101184*a(n-11) -3510669312*a(n-12) -15177555968*a(n-13) +15458697216*a(n-14) +13446168576*a(n-15) -14442954752*a(n-16) -4507631616*a(n-17) +3989831680*a(n-18) +252706816*a(n-19) -251658240*a(n-20) for n>25.

A223485 Rolling icosahedron face footprints: number of 7Xn 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves across an icosahedral edge.

Original entry on oeis.org

64000000, 1594323, 102515625, 6591796875, 563999907825, 48783753036675, 4468456626780825, 409807503225524475, 38120535124295537025, 3545335226678204077875, 330863549667143315488425

Offset: 1

R. H. Hardin Mar 20 2013

nonn

Row 7 of A223480

			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..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0
..0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..4
..0..5..7....4..1..4....4..1..6....4..1..4....6..1..4....4..1..6....4.17..4
..7..5..7....6..1..0....6..7..5....6..1..6....6..1..6....0..1..4....4..3.16
..9..5..7....0..5..9...11..7.11....0..1..0....0..1..0....4.17.18....2..3..4
..0..5..9....9.14.11...11.12.10....6..1..0....0..5..9....4.17.10...16..3..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..36

A223476 Rolling icosahedron face footprints: number of n X n 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves across an icosahedral edge.

Original entry on oeis.org

1, 27, 2025, 421875, 288507825, 622332801675, 4468456626780825, 104443823338086658275, 8163685522687864520397825, 2101858460730043160691131026875

Offset: 1

R. H. Hardin Mar 20 2013

nonn

Diagonal of A223480

			Some solutions for n=3
..0..1..0....0..2..8....0..2..8....0..2..8....0..2..8....0..2..8....0..2..8
..0..5..7....8..9.14....0..2..3....0..2..8....0..2..0....3..2..8....8..2..3
..7..5..9...14.11..7....3..4.17....8..2..8....3..2..0....3..2..3....3..4..3
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

cp's OEIS Frontend

A223477 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 or antidiagonal neighbor moves across an icosahedral edge.

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A223478 Rolling icosahedron face footprints: number of n X 6 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves across an icosahedral edge.

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A223479 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 or antidiagonal neighbor moves across an icosahedral edge.

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A223481 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 or antidiagonal neighbor moves across an icosahedral edge.

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A223482 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 or antidiagonal neighbor moves across an icosahedral edge.

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A223483 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 or antidiagonal neighbor moves across an icosahedral edge.

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A223484 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 or antidiagonal neighbor moves across an icosahedral edge.

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A223485 Rolling icosahedron face footprints: number of 7Xn 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves across an icosahedral edge.

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A223476 Rolling icosahedron face footprints: number of n X n 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves across an icosahedral edge.

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