cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

A223434 Generalized Petersen graph (8,2) coloring a rectangular array: number of n X 2 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

Original entry on oeis.org

48, 256, 1376, 7424, 40160, 217600, 1180256, 6405888, 34782688, 188912640, 1026197344, 5575016704, 30289360608, 164570543616, 894181114976, 4858543170304, 26399224399840, 143442922485760, 779415220762976
Offset: 1

Views

Author

R. H. Hardin, Mar 20 2013

Keywords

Comments

Column 2 of A223440.

Examples

			Some solutions for n=3:
..6..5....8..0....3..4...11.13....7..0...11.13....9..1....1..0....1..9....1..9
.14..6....0..7....2..3...13.15...15..7...13.15....1..2....0..1....2..1....9.11
..8.14....8..0....3..2...15.13....9.15...15..7....2..3....1..2....3..2....1..9
		

Crossrefs

Cf. A223440.

Formula

Empirical: a(n) = 8*a(n-1) - 11*a(n-2) - 16*a(n-3).
Empirical g.f.: 16*x*(3 - 8*x - 9*x^2) / (1 - 8*x + 11*x^2 + 16*x^3). - Colin Barker, Mar 16 2018

A223435 Generalized Petersen graph (8,2) coloring a rectangular array: number of nX3 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

Original entry on oeis.org

144, 1376, 14112, 147520, 1562176, 16693920, 179532768, 1939216640, 21008925952, 228065409888, 2479179661472, 26974655289536, 293678536506304, 3198664399776288, 34848651790913888, 379738193353123456
Offset: 1

Views

Author

R. H. Hardin Mar 20 2013

Keywords

Comments

Column 3 of A223440

Examples

			Some solutions for n=3
.13.11.13....9.11..9...12..4..5....9.15.13....6..5.13....5..6.14....6..5..6
.15..9.11....1..9..1....4..3..4...15..9.11....7..6..5....6.14.12....5..6..7
.13.11.13....0..1..2....5..4.12....9.15.13....0..7..6...14.12.14....6.14..6
		

Formula

Empirical: a(n) = 15*a(n-1) -18*a(n-2) -310*a(n-3) +167*a(n-4) +475*a(n-5) -244*a(n-6) -100*a(n-7) +48*a(n-8)

A223436 Generalized Petersen graph (8,2) coloring a rectangular array: number of n X 4 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

Original entry on oeis.org

432, 7424, 147520, 3099264, 67182208, 1485628224, 33277934848, 751557814208, 17060996532992, 388541047749184, 8866017102928512, 202557753134780608, 4631201059795429632, 105934451744168513600, 2423832070620348866432
Offset: 1

Views

Author

R. H. Hardin, Mar 20 2013

Keywords

Comments

Column 4 of A223440.

Examples

			Some solutions for n=3
..8..0..8.14....7..6..7..0....4.12..4..3....6..7..6..5...14..8.10.12
.14..8..0..8....6..7.15..7....5..4..5..4....5..6..7..6....8.14..8.10
.12.14..8..0....7.15..9.15....4.12..4..5....6.14..6..5...10.12.10..2
		

Crossrefs

Cf. A223440.

Formula

Empirical: a(n) = 37*a(n-1) -272*a(n-2) -2014*a(n-3) +20537*a(n-4) -19463*a(n-5) -166878*a(n-6) +279708*a(n-7) +430814*a(n-8) -869500*a(n-9) -281352*a(n-10) +853376*a(n-11) -53696*a(n-12) -245568*a(n-13) +62720*a(n-14).

A223437 Generalized Petersen graph (8,2) coloring a rectangular array: number of nX5 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

Original entry on oeis.org

1296, 40160, 1562176, 67182208, 3049973040, 142702806112, 6790055219264, 326095786136512, 15740601974728144, 761894144429277728, 36933075864379992960, 1791784217341289032832, 86964938378374308543408
Offset: 1

Views

Author

R. H. Hardin Mar 20 2013

Keywords

Comments

Column 5 of A223440

Examples

			Some solutions for n=3
.14.12.14.12.10...14..8..0..7..0...14..8.10.12..4...10.12.10.12.14
..8.14..8.14..8....8..0..7.15..7....6.14..8.14.12....2.10..2.10..8
..0..8.14..8..0....0..7.15..7..6...14..8.14.12..4...10.12.10..2.10
		

Formula

Empirical: a(n) = 62*a(n-1) +97*a(n-2) -43361*a(n-3) +169107*a(n-4) +9430075*a(n-5) -42692985*a(n-6) -944380223*a(n-7) +4270354567*a(n-8) +50259902237*a(n-9) -223620107693*a(n-10) -1517318142163*a(n-11) +6782196814489*a(n-12) +26682637399469*a(n-13) -124450548676359*a(n-14) -271316347782785*a(n-15) +1405146906215354*a(n-16) +1486735261657557*a(n-17) -9731248121419764*a(n-18) -3199983254595948*a(n-19) +40528119973374804*a(n-20) -5730916061514328*a(n-21) -98589639864853568*a(n-22) +43705272486463008*a(n-23) +135607659234364992*a(n-24) -89468393018269056*a(n-25) -98957223312948992*a(n-26) +87411803248288256*a(n-27) +31094370745832448*a(n-28) -42403903770849280*a(n-29) +555544355516416*a(n-30) +9031467111268352*a(n-31) -2014501576998912*a(n-32) -534258356224000*a(n-33) +246552412291072*a(n-34) -28053544108032*a(n-35) +759655563264*a(n-36)

A223438 Generalized Petersen graph (8,2) coloring a rectangular array: number of nX6 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

Original entry on oeis.org

3888, 217600, 16693920, 1485628224, 142702806112, 14233389951648, 1445484467129440, 148051853028192512, 15224711042202343552, 1568546471897589578240, 161743493137179916579328
Offset: 1

Views

Author

R. H. Hardin Mar 20 2013

Keywords

Comments

Column 6 of A223440

Examples

			Some solutions for n=3
..8.10.12.10..2.10....8.10..8.14.12..4....8.10..8..0..7..0....8..0..8.14..8..0
..0..8.10..2..1..2....0..8.10.12.14.12....0..8.10..8..0..7....0..8.10..8.10..8
..8.14..8.10..2..1....8.10.12.10.12.10....8..0..8..0..8..0....8..0..8.14.12.10
		

Formula

Empirical: a(n) = 179*a(n-1) -6951*a(n-2) -271607*a(n-3) +21119701*a(n-4) -118613501*a(n-5) -16042793190*a(n-6) +277619145432*a(n-7) +4774235776970*a(n-8) -143405382746884*a(n-9) -420821388852096*a(n-10) +37606839411196966*a(n-11) -108407551854657226*a(n-12) -5925717179937776746*a(n-13) +39180449352667077880*a(n-14) +594191118931902297380*a(n-15) -6048293242384810531005*a(n-16) -37425103625741440759549*a(n-17) +581628683844798046438773*a(n-18) +1237091247316116764955769*a(n-19) -38359293135928763955100103*a(n-20) +10460671769010555148095519*a(n-21) +1803003415972858635750111358*a(n-22) -3555491137079607222972056260*a(n-23) -61240750606527318395511648092*a(n-24) +208929828925354587554180034318*a(n-25) +1496274712129237698547575636186*a(n-26) -7383850296772908334765122622272*a(n-27) -25486824081243026489791296763924*a(n-28) +180945378839552150289431909848184*a(n-29) +272060798461933104708902120861352*a(n-30) -3223625701824336396853308761486432*a(n-31) -926992300176834952990672970545568*a(n-32) +42605028363187490241072310143295696*a(n-33) -24181387384720951667537133460117088*a(n-34) -421243983113204347458262866291111104*a(n-35) +522621268456758965922986474070191680*a(n-36) +3117652620410103561192249896061440704*a(n-37) -5757985944132377746954418458709319168*a(n-38) -17136186963844437148251471189604363776*a(n-39) +42807061143532148618500747175742229248*a(n-40) +68360313318415840393673365396945673728*a(n-41) -230878479976506864281497267126776039424*a(n-42) -185958383458129096930882467989236291584*a(n-43) +929638490630874241066066348711815901184*a(n-44) +272642333553193345312255046530514829312*a(n-45) -2828506494259520326303069238640433889280*a(n-46) +187876400515135304183018125265604706304*a(n-47) +6522259870842702958321466972861679337472*a(n-48) -2199835759024541218671700798961932042240*a(n-49) -11351796940281836861931047881940781760512*a(n-50) +6326111340620304034339570888129924038656*a(n-51) +14742943903606817466073273582029857882112*a(n-52) -11131170323309421129817159596245627437056*a(n-53) -13982019244531593213598483709829966725120*a(n-54) +13446193221349424784824942171525176360960*a(n-55) +9302529715774949884948586274845993467904*a(n-56) -11465865042568043262964603473706725933056*a(n-57) -3978202072362133000934554075141704253440*a(n-58) +6894264763275498221487759159674638696448*a(n-59) +804438912205355891400653311864345722880*a(n-60) -2870777348120732309785811350967050829824*a(n-61) +136108470483921596342924067271644020736*a(n-62) +799525309855040342220275767358101913600*a(n-63) -138526363297520598455023112398047281152*a(n-64) -140099281831814052898932707279947956224*a(n-65) +39805653154762055884979103573022343168*a(n-66) +13633601779888820299846675388669362176*a(n-67) -5739652518611612105149682128970055680*a(n-68) -485708260970010936160701727360679936*a(n-69) +409698635146914391412410184502345728*a(n-70) -18064072479780486906434123536007168*a(n-71) -11446924048860749714664666544734208*a(n-72) +1296574284601992775674928708976640*a(n-73) +38674149510563025837725853941760*a(n-74) -6774069712859013824343598694400*a(n-75)

A223439 Generalized Petersen graph (8,2) coloring a rectangular array: number of nX7 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

Original entry on oeis.org

11664, 1180256, 179532768, 33277934848, 6790055219264, 1445484467129440, 313233804577725904, 68373044838570536416, 14968850924351337707600, 3281073242585313313486816, 719543293998612435740651440
Offset: 1

Views

Author

R. H. Hardin Mar 20 2013

Keywords

Comments

Column 7 of A223440

Examples

			Some solutions for n=3
..8..0..8.14..8.14..8....8..0..8.14.12.10.12....8..0..8.10.12.14..8
..0..8.14..8.10..8.10....0..8.14..8.10.12.14....0..8.10..8.14.12.10
..8..0..8..0..8.10..2....8..0..8.10..8.10..8....8..0..8.14.12.10..8
		

A223433 Generalized Petersen graph (8,2) coloring a rectangular array: number of n X n 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

Original entry on oeis.org

16, 256, 14112, 3099264, 3049973040, 14233389951648, 313233804577725904, 31773869927610747929664, 14659288101904896523559420400, 30618348337161405692150233995935392
Offset: 1

Views

Author

R. H. Hardin Mar 20 2013

Keywords

Comments

Diagonal of A223440

Examples

			Some solutions for n=3
..6..7.15...15.13.11....4..5..6....3..4..5....4.12..4...10..8.10...15.13.11
..7..0..7...13.15..9....5..6..7....4..5..4....5..4..5...12.10..8...13.11.13
..6..7..0...15..9.11....6..7..6....5..6..5....4..5.13....4.12.14...15..9.15
		
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