A223321 -id:A223321 - cp's OEIS frontend

A223318 Rolling icosahedron footprints: number of n X 5 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

625, 274625, 122039125, 54279694625, 24143758634125, 10739266230499625, 4776881955584279125, 2124782217358970404625, 945114307570509938324125, 420391815800244320602909625, 186992491150169573406883769125

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Column 5 of A223321.

			Some solutions for n=3:
..0..6..2..6.10....0..6..2..6..0....0..6.10..6..0....0..6..0..1..3
..0..6..0..6..2....0..6..0..6..2....0..6..0..2..4....0..6..2..8..2
..0..1..0..1..3....0..1..2..1..0....0..2..4.10..4....0..1..2..4..8
Vertex neighbors:
0 -> 1 2 5 6 7
1 -> 0 2 3 7 8
2 -> 0 1 4 6 8
3 -> 1 7 8 9 11
4 -> 2 6 8 9 10
5 -> 0 6 7 10 11
6 -> 0 2 4 5 10
7 -> 0 1 3 5 11
8 -> 1 2 3 4 9
9 -> 3 4 8 10 11
10 -> 4 5 6 9 11
11 -> 3 5 7 9 10

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

Cf. A223321.

Empirical: a(n) = 479*a(n-1) - 15210*a(n-2).
Conjectures from Colin Barker, Aug 19 2018: (Start)
G.f.: 125*x*(5 - 198*x) / (1 - 479*x + 15210*x^2).
a(n) = (25*2^(-1-n)*((479-sqrt(168601))^n*(-3181+11*sqrt(168601)) + (479+sqrt(168601))^n*(3181+11*sqrt(168601)))) / (169*sqrt(168601)).
(End)

A223319 Rolling icosahedron footprints: number of n X 6 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

Original entry on oeis.org

3125, 3570125, 4176940625, 4903804407125, 5759605530667625, 6765094542682458125, 7946162712131677450625, 9333430848774501484101125, 10962893764533341367143473625, 12876834103685350223700565272125

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Column 6 of A223321.

			Some solutions for n=3:
..0..6..0..6..0..5....0..6..0..1..8..2....0..6..0..6..0..2....0..6..0..6..0..2
..0..6..0..5..6..4....0..6..0..2..0..6....0..6..0..1..8..3....0..6..0..5..0..7
..0..1..7..5.10.11....0..1..0..2..4..8....0..1..3..9..8..3....0..1..7..1..3..7
Vertex neighbors:
0 -> 1 2 5 6 7
1 -> 0 2 3 7 8
2 -> 0 1 4 6 8
3 -> 1 7 8 9 11
4 -> 2 6 8 9 10
5 -> 0 6 7 10 11
6 -> 0 2 4 5 10
7 -> 0 1 3 5 11
8 -> 1 2 3 4 9
9 -> 3 4 8 10 11
10 -> 4 5 6 9 11
11 -> 3 5 7 9 10

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

Cf. A223321.

Empirical: a(n) = 1366*a(n-1) - 232713*a(n-2) + 9253764*a(n-3).

Empirical g.f.: 125*x*(25 - 5589*x + 219024*x^2) / (1 - 1366*x + 232713*x^2 - 9253764*x^3). - Colin Barker, Aug 19 2018

A223320 Rolling icosahedron footprints: number of nX7 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

Original entry on oeis.org

15625, 46411625, 142980696625, 443803619416625, 1379464144963464625, 4288761014162797342625, 13334277936752000032650625, 41458126974532997739670258625, 128899204399783389165401518452625

Offset: 1

R. H. Hardin Mar 19 2013

nonn

Column 7 of A223321

			Some solutions for n=3
..0..6..0..6..0..1..2....0..6..0..6..0..1..2....0..6..0..6..0..6..2
..0..6..0..6..0..1..3....0..6..0..6..2..6..5....0..6..0..6.10..6.10
..0..6..0..7..3..7..1....0..6..0..6..4..6..4....0..6..0..6..5..6.10
Vertex neighbors:
0 -> 1 2 5 6 7
1 -> 0 2 3 7 8
2 -> 0 1 4 6 8
3 -> 1 7 8 9 11
4 -> 2 6 8 9 10
5 -> 0 6 7 10 11
6 -> 0 2 4 5 10
7 -> 0 1 3 5 11
8 -> 1 2 3 4 9
9 -> 3 4 8 10 11
10 -> 4 5 6 9 11
11 -> 3 5 7 9 10

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

Empirical: a(n) = 4313*a(n-1) -4293540*a(n-2) +1835925129*a(n-3) -400542201531*a(n-4) +46506128233194*a(n-5) -2762797384141236*a(n-6) +72983536818080616*a(n-7) -643864107456947520*a(n-8)

A223322 Rolling icosahedron footprints: number of 2 X n 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

Original entry on oeis.org

12, 125, 1625, 21125, 274625, 3570125, 46411625, 603351125, 7843564625, 101966340125, 1325562421625, 17232311481125, 224020049254625, 2912260640310125, 37859388324031625, 492172048212411125

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Row 2 of A223321.

			Some solutions for n=3:
..0..7..3....0..2..8....0..2..4....0..5.11....0..6..5....0..1..3....0..7..0
..1..8..4....8..1..2....8..2..1...10..9..4....2..6..2....3.11..3....0..1..7
Vertex neighbors:
0 -> 1 2 5 6 7
1 -> 0 2 3 7 8
2 -> 0 1 4 6 8
3 -> 1 7 8 9 11
4 -> 2 6 8 9 10
5 -> 0 6 7 10 11
6 -> 0 2 4 5 10
7 -> 0 1 3 5 11
8 -> 1 2 3 4 9
9 -> 3 4 8 10 11
10 -> 4 5 6 9 11
11 -> 3 5 7 9 10

R. H. Hardin, Table of n, a(n) for n = 1..210
Index entries for linear recurrences with constant coefficients, signature (13).

Cf. A223321.

Empirical: a(n) = 13*a(n-1) for n>2.
Conjectures from Colin Barker, Aug 19 2018: (Start)
G.f.: x*(12 - 31*x) / (1 - 13*x).
a(n) = 125*13^(n-2) for n>1.
(End)

A223323 Rolling icosahedron footprints: number of 3 X n 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

Original entry on oeis.org

144, 3125, 105625, 3570125, 122039125, 4176940625, 142980696625, 4894441131125, 167544253118125, 5735298712573625, 196328142425559625, 6720615878249268125, 230057073000574997125, 7875209325727694302625, 269580591960578208870625

Offset: 1

R. H. Hardin, Mar 19 2013

nonn

Row 3 of A223321.

			Some solutions for n=3:
..0..6..5....0..7..3....0..1..8....0..7.11....0..7.11....0..7..1....0..7..1
..4.10..4....3..8..2....0..1..8....3..7..3....0..7..1....1..2..8....1..8..4
.11..9..3....1..8..1....2..1..2....3..9..8...11..3..7....0..1..7....9..8..4
Vertex neighbors:
0 -> 1 2 5 6 7
1 -> 0 2 3 7 8
2 -> 0 1 4 6 8
3 -> 1 7 8 9 11
4 -> 2 6 8 9 10
5 -> 0 6 7 10 11
6 -> 0 2 4 5 10
7 -> 0 1 3 5 11
8 -> 1 2 3 4 9
9 -> 3 4 8 10 11
10 -> 4 5 6 9 11
11 -> 3 5 7 9 10

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

Cf. A223321.

Empirical: a(n) = 38*a(n-1) - 129*a(n-2) for n>4.

Empirical g.f.: x*(144 - 2347*x + 5451*x^2 - 40500*x^3) / (1 - 38*x + 129*x^2). - Colin Barker, Aug 19 2018

A223324 Rolling icosahedron footprints: number of 4Xn 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

Original entry on oeis.org

1728, 78125, 6865625, 603351125, 54279694625, 4903804407125, 443803619416625, 40180564679055125, 3638107937069854625, 329414029399378035125, 29827030198435983748625, 2700711676390250182863125

Offset: 1

R. H. Hardin Mar 19 2013

nonn

Row 4 of A223321

			Some solutions for n=3
..0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0
..0..5..7....0..1..3....0..1..8....0..6.10....0..7.11....0..6..5....0..1..2
..0..5..6....3..8..2....2..1..3....4..9..8...11..7..0....2..0..2....0..6..0
.10..5..0....4..6..2....3..9.11....8..4..6....1..2..0....2..8..1....0..1..3
Vertex neighbors:
0 -> 1 2 5 6 7
1 -> 0 2 3 7 8
2 -> 0 1 4 6 8
3 -> 1 7 8 9 11
4 -> 2 6 8 9 10
5 -> 0 6 7 10 11
6 -> 0 2 4 5 10
7 -> 0 1 3 5 11
8 -> 1 2 3 4 9
9 -> 3 4 8 10 11
10 -> 4 5 6 9 11
11 -> 3 5 7 9 10

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

Empirical: a(n) = 121*a(n-1) -3029*a(n-2) +25559*a(n-3) -89707*a(n-4) +122263*a(n-5) -12831*a(n-6) -60039*a(n-7) for n>10

A223325 Rolling icosahedron footprints: number of 5Xn 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

Original entry on oeis.org

20736, 1953125, 446265625, 101966340125, 24143758634125, 5759605530667625, 1379464144963464625, 330817503041200989125, 79372689616849936523125, 19046505898852803312046625, 4570642727979496865778147625

Offset: 1

R. H. Hardin Mar 19 2013

nonn

Row 5 of A223321

			Some solutions for n=3
..0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0
..0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0
..0..5..7....0..5..7....0..6..5....0..1..0....0..7..3....0..5.10....0..7..0
..0..5..6...10.11..7....4..6..5....0..6..5...11..9..4...10..6..0....1..7..1
..6..0..7....5.11.10...10..6..0....4..6..0...10..9..8....0..1..7...11..3..9
Vertex neighbors:
0 -> 1 2 5 6 7
1 -> 0 2 3 7 8
2 -> 0 1 4 6 8
3 -> 1 7 8 9 11
4 -> 2 6 8 9 10
5 -> 0 6 7 10 11
6 -> 0 2 4 5 10
7 -> 0 1 3 5 11
8 -> 1 2 3 4 9
9 -> 3 4 8 10 11
10 -> 4 5 6 9 11
11 -> 3 5 7 9 10

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

Empirical: a(n) = 410*a(n-1) -51839*a(n-2) +2998354*a(n-3) -88929070*a(n-4) +1198807214*a(n-5) +2889121905*a(n-6) -340756682572*a(n-7) +4538793109678*a(n-8) -13887817317962*a(n-9) -242674670034177*a(n-10) +2612400275589524*a(n-11) -4250937817051838*a(n-12) -72579353969012690*a(n-13) +404852006352195731*a(n-14) +294243010726671144*a(n-15) -8038059311698199807*a(n-16) +14527240098893219908*a(n-17) +63207106281330811172*a(n-18) -241285400707856322796*a(n-19) -99441316590244134158*a(n-20) +1499939986936247507922*a(n-21) -1264768034332853154292*a(n-22) -3709575277042038429058*a(n-23) +6249708500546392632287*a(n-24) +1712083980241985550010*a(n-25) -7806673210840206689815*a(n-26) +1552725322135658220450*a(n-27) +3587994096679078794377*a(n-28) -1272290169371896871744*a(n-29) -473135759143977735225*a(n-30) +224855787210470741790*a(n-31) -20543329382473731600*a(n-32) for n>36

A223326 Rolling icosahedron footprints: number of 6Xn 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

Original entry on oeis.org

248832, 48828125, 29007265625, 17232311481125, 10739266230499625, 6765094542682458125, 4288761014162797342625, 2725466174591233186641125, 1733931516143286321479437625, 1103604638130169667481962994125

Offset: 1

R. H. Hardin Mar 19 2013

nonn

Row 6 of A223321

			Some solutions for n=3
..0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0
..0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0
..0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0....0..6..0
..0..1..0....0..2..1....0..1..8....0..6..4....0..2..1....0..1..2....0..7.11
..7..1..0....1..0..2....8..3..1....4..2..0....1..8..2....8..4..2....5..7..3
..3..1..0....1..8..2....9..3..8....0..7..3....2..6..2....8..4.10....3..7..0
Vertex neighbors:
0 -> 1 2 5 6 7
1 -> 0 2 3 7 8
2 -> 0 1 4 6 8
3 -> 1 7 8 9 11
4 -> 2 6 8 9 10
5 -> 0 6 7 10 11
6 -> 0 2 4 5 10
7 -> 0 1 3 5 11
8 -> 1 2 3 4 9
9 -> 3 4 8 10 11
10 -> 4 5 6 9 11
11 -> 3 5 7 9 10

R. H. Hardin, Table of n, a(n) for n = 1..89

cp's OEIS Frontend

A223318 Rolling icosahedron footprints: number of n X 5 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

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A223319 Rolling icosahedron footprints: number of n X 6 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

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A223320 Rolling icosahedron footprints: number of nX7 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

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A223322 Rolling icosahedron footprints: number of 2 X n 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

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A223323 Rolling icosahedron footprints: number of 3 X n 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

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A223324 Rolling icosahedron footprints: number of 4Xn 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

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A223325 Rolling icosahedron footprints: number of 5Xn 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

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A223326 Rolling icosahedron footprints: number of 6Xn 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.

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