A223233 -id:A223233 - cp's OEIS frontend

A223228 Rolling icosahedron footprints: number of n X 3 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge.

25, 785, 25225, 812225, 26157625, 842416625, 27130395625, 873746350625, 28139386665625, 906241361740625, 29185902861015625, 939944877578890625, 30271339457769765625, 974901842039841640625, 31397143920195178515625

Offset: 1

R. H. Hardin, Mar 18 2013

nonn

Column 3 of A223233.

			Some solutions for n=3:
..0..7.11....0..7.11....0..6.10....0..7..0....0..2..0....0..2..0....0..6..4
..3..7..3....3..7..1....2..6..2...11..7..1....0..7..0....0..6..4....4..2..4
.11..7.11....5..7..3....2..4..2....0..7..5...11..7..3....4..2..0....8..9..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. A223233.

Empirical: a(n) = 35*a(n-1) - 90*a(n-2).
Conjectures from Colin Barker, Aug 17 2018: (Start)
G.f.: 5*x*(5 - 18*x) / (1 - 35*x + 90*x^2).
a(n) = (2^(-1-n)*((35-sqrt(865))^n*(-15+sqrt(865)) + (15+sqrt(865))*(35+sqrt(865))^n)) / sqrt(865).
(End)

A223229 Rolling icosahedron footprints: number of n X 4 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge.

Original entry on oeis.org

125, 7445, 492365, 32837285, 2191464605, 146259564725, 9761484584045, 651489782832965, 43480983274973885, 2901957882023749205, 193679142376194109325, 12926311034495639900645, 862713015509641940473565

Offset: 1

R. H. Hardin, Mar 18 2013

nonn

Column 4 of A223233.

			Some solutions for n=3:
..0..6.10..5....0..5..7..0....0..5..0..7....0..1..7..5....0..2..4..2
..0..6.10..6....0..5..7..3....6..5..0..6....0..1..7..5....6..2..8..9
..0..6..5..6....0..5..7..3....0..2..0..5....3..1..7..0....0..2..8..1
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. A223233.

Empirical: a(n) = 73*a(n-1) - 423*a(n-2) + 351*a(n-3).

Empirical g.f.: 5*x*(25 - 336*x + 351*x^2) / ((1 - x)*(1 - 72*x + 351*x^2)). - Colin Barker, Aug 17 2018

A223230 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, diagonal or antidiagonal neighbor moves along an icosahedral edge.

Original entry on oeis.org

625, 75665, 11043445, 1697263985, 266409703885, 42210625593305, 6716507564288245, 1070788920090847265, 170861214141424879645, 27274345271819338522025, 4354541372254902852256645

Offset: 1

R. H. Hardin Mar 18 2013

nonn

Column 5 of A223233.

			Some solutions for n=3
..0..2..4.10..4....0..5..0..2..4....0..6..2..0..1....0..5..6..0..2
..6..2..6.10.11....6..2..6..2..6....0..6..2..8..2....6..2..6..4..6
..1..0..6.10..5....1..0..1..2..0....0..6..2..1..2....6..0..6..2..6
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. A223233.

Empirical: a(n) = 251*a(n-1) -15873*a(n-2) +195175*a(n-3) +2042368*a(n-4) -47798442*a(n-5) +263976930*a(n-6) -451699632*a(n-7) -350892000*a(n-8) +1964608344*a(n-9) -2144659680*a(n-10) +765275040*a(n-11).

A223231 Rolling icosahedron footprints: number of nX6 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge.

Original entry on oeis.org

3125, 753005, 236027705, 78951770585, 27049155640325, 9343721361109325, 3237164242739054345, 1122694859942471556185, 389510525064654891088085, 135155431698699358247850605, 46899472272729726654991007705

Offset: 1

R. H. Hardin Mar 18 2013

nonn

Column 6 of A223233

			Some solutions for n=3
..0..6..0..5..6.10....0..6..0..1..0..1....0..6..4..2..0..2....0..6..0..2..0..2
..0..6..0..5..6..5....0..6..0..1..0..5....0..6..0..2..0..7....0..6..0..7..0..7
..0..6..0..5..6..2....0..6..0..1..7..1....0..6..0..7..1..7....0..6..0..2..0..2
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) = 525*a(n-1) -66702*a(n-2) +1331899*a(n-3) +153275287*a(n-4) -7341587858*a(n-5) +30374971203*a(n-6) +3824146236752*a(n-7) -75111050134232*a(n-8) +205037655577424*a(n-9) +6460684913361019*a(n-10) -49290095118307364*a(n-11) -140021336623195442*a(n-12) +2200689678890462843*a(n-13) -1458667313500165314*a(n-14) -37187688159845953965*a(n-15) +75037715810598760272*a(n-16) +230357416636661884542*a(n-17) -652626536223111303870*a(n-18) -496313838990773846658*a(n-19) +2029968756189631881972*a(n-20) +256192718593072185252*a(n-21) -2481072401873869960176*a(n-22) +64389835845560317824*a(n-23) +1236374401394896182000*a(n-24) -45277328877999388704*a(n-25) -205116615409293840384*a(n-26)

A223232 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, diagonal or antidiagonal neighbor moves along an icosahedral edge.

Original entry on oeis.org

15625, 7540985, 5127809545, 3843057179285, 3010781803380625, 2410480042269361205, 1952463524081506924645, 1591754706579747811787945, 1302463364554005567144837065, 1067991482533134242042535939665

Offset: 1

R. H. Hardin Mar 18 2013

nonn

Column 7 of A223233

			Some solutions for n=3
..0..6..0..6..0..6..0....0..6..0..5..0..1..2....0..6..0..6..4..8..2
..0..6..0..6..0..7..0....0..6..0..6..0..6..2....0..6..0..6..2..8..3
..0..6..0..1..0..2..0....0..6..0..6..5..6..0....0..6..0..6..2..8..1
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..110

A223234 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, diagonal or antidiagonal neighbor moves along an icosahedral edge.

Original entry on oeis.org

12, 65, 785, 7445, 75665, 753005, 7540985, 75377045, 753868865, 7538393405, 75384819785, 753845540645, 7538463378065, 75384609865805, 753846170402585, 7538461488792245, 75384615533623265, 753846153399130205

Offset: 1

R. H. Hardin, Mar 18 2013

nonn

Row 2 of A223233.

			Some solutions for n=3:
..0..2..1....0..7.11....0..6..2....0..6..5....0..7..3....0..2..1....0..2..0
..0..7..0....3..7..3...10..6..4....4..6..5....3..7..0....6..2..8....8..2..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. A223233.

Empirical: a(n) = 7*a(n-1) + 30*a(n-2) for n>3.
Conjectures from Colin Barker, Aug 17 2018: (Start)
G.f.: x*(12 - 19*x - 30*x^2) / ((1 + 3*x)*(1 - 10*x)).
a(n) = (-25*(-1)^n*3^(1+n) + 49*10^n) / 65 for n>1.
(End)

A223235 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, diagonal or antidiagonal neighbor moves along an icosahedral edge.

Original entry on oeis.org

144, 845, 25225, 492365, 11043445, 236027705, 5127809545, 110781320885, 2397904326205, 51869658014705, 1122255717889585, 24279356422739885, 525283571663978725, 11364402460546714985, 245867265513538637785

Offset: 1

R. H. Hardin, Mar 18 2013

nonn

Row 3 of A223233.

			Some solutions for n=3:
..0..2..0....0..5..7....0..6..2....0..2..1....0..6..0....0..1..7....0..1..7
..0..5..0....0..5..6....0..6..5....1..2..6....0..6..0....0..1..3....0..1..8
.11..5..0....0..5..6....5..7..0....4..2..1....4..2..0....3..7..0....7..1..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. A223233.

Empirical: a(n) = 18*a(n-1) + 103*a(n-2) - 552*a(n-3) + 540*a(n-4) for n>5.

Empirical g.f.: x*(144 - 1747*x - 4817*x^2 + 30768*x^3 - 28620*x^4) / (1 - 18*x - 103*x^2 + 552*x^3 - 540*x^4). - Colin Barker, Aug 17 2018

A223236 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, diagonal or antidiagonal neighbor moves along an icosahedral edge.

Original entry on oeis.org

1728, 10985, 812225, 32837285, 1697263985, 78951770585, 3843057179285, 183367303999865, 8826695677742465, 423223089093370325, 20328307272501475145, 975647469218575594625, 46842159188887320714725

Offset: 1

R. H. Hardin Mar 18 2013

nonn

Row 4 of A223233

			Some solutions for n=3
..0..6.10....0..6..0....0..6..4....0..6.10....0..6.10....0..6..2....0..6..0
..4..6..4....0..7..0....4..6..2...10..6..0....4..6..0....0..6..2....4..6..0
..5..6..2....3..7..1....5..6..0....4..6..4....5..6..2....2..6..4....2..6..4
..5..0..2....5..7..3....5..6..0....5.10..5....2..6..0....5..6..0...10..6..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

Empirical: a(n) = 32*a(n-1) +1042*a(n-2) -11074*a(n-3) -125832*a(n-4) +1314816*a(n-5) -820893*a(n-6) -14900218*a(n-7) +19327896*a(n-8) +41119416*a(n-9) -33578064*a(n-10) -26034048*a(n-11) +12597120*a(n-12) for n>13

A223237 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, diagonal or antidiagonal neighbor moves along an icosahedral edge.

Original entry on oeis.org

20736, 142805, 26157625, 2191464605, 266409703885, 27049155640325, 3010781803380625, 319668431152592585, 34788800528856366205, 3737470592349481922045, 404261376372354175571785

Offset: 1

R. H. Hardin Mar 18 2013

nonn

Row 5 of A223233

			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...10..6..0....4..6..0....0..6..0....4..6..0....0..6..0....4..6..0
..0..2..0....0..6..2....5..6..0....0..5.10...10..6..2....0..7..5....0..6..4
..0..5..0...10..6..4....0..7..5....0..5..6....5..6..4....0..6..5....4..2..0
..6..5..6...10..6..5....0..7.11....0..5.10....0..6..5....2..6..4....0..2..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

A223238 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, diagonal or antidiagonal neighbor moves along an icosahedral edge.

Original entry on oeis.org

248832, 1856465, 842416625, 146259564725, 42210625593305, 9343721361109325, 2410480042269361205, 569856683384487837845, 141861478546517230929185, 34264186727962091778301265, 8425769874595179617059603645

Offset: 1

R. H. Hardin Mar 18 2013

nonn

Row 6 of A223233

			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
..2..6..0....0..6..0....0..6..0....0..6..0....2..6..0....4..6..0....2..6..0
..0..6.10....0..7..5....0..5.10....2..1..0....4..6..4....4..2..0....0..6..2
.10..6.10....0..6..0...11..5.11....8..1..0....4..6..5....8..2..6....4..6..5
.10..4..2....0..7..0...11..5..6....8..1..0....5..6.10....1..2..1....4..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..36

cp's OEIS Frontend

A223228 Rolling icosahedron footprints: number of n X 3 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge.

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A223229 Rolling icosahedron footprints: number of n X 4 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge.

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A223230 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, diagonal or antidiagonal neighbor moves along an icosahedral edge.

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A223231 Rolling icosahedron footprints: number of nX6 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge.

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A223232 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, diagonal or antidiagonal neighbor moves along an icosahedral edge.

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A223234 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, diagonal or antidiagonal neighbor moves along an icosahedral edge.

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A223235 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, diagonal or antidiagonal neighbor moves along an icosahedral edge.

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A223236 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, diagonal or antidiagonal neighbor moves along an icosahedral edge.

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A223237 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, diagonal or antidiagonal neighbor moves along an icosahedral edge.

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A223238 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, diagonal or antidiagonal neighbor moves along an icosahedral edge.

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