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 1-8 of 8 results.

A189247 Number of n X 2 array permutations with each element making zero or one king moves.

Original entry on oeis.org

2, 24, 152, 1168, 8448, 62272, 456320, 3350016, 24579584, 180376576, 1323614208, 9712930816, 71274930176, 523026923520, 3838053810176, 28164247060480, 206673697308672, 1516604287614976, 11129082140426240, 81666965136998400
Offset: 1

Views

Author

R. H. Hardin, Apr 19 2011

Keywords

Comments

Column 2 of A189254.

Examples

			Some solutions for 3 X 2:
..1..2....1..2....1..2....3..1....0..1....1..0....0..2....2..0....2..1....0..1
..0..3....0..4....3..0....5..0....4..2....3..2....3..1....5..1....3..0....3..5
..5..4....5..3....4..5....4..2....3..5....5..4....4..5....4..3....4..5....2..4
		

Crossrefs

Cf. A189254.

Formula

Empirical: a(n) = 6*a(n-1) + 12*a(n-2) - 16*a(n-3).
Empirical g.f.: 2*x*(1 + 6*x - 8*x^2) / (1 - 6*x - 12*x^2 + 16*x^3). - Colin Barker, Mar 01 2018

A189248 Number of nX3 array permutations with each element making zero or one king moves.

Original entry on oeis.org

3, 152, 2961, 76629, 1818336, 44308389, 1070959431, 25950094568, 628311228261, 15216392096673, 368483172355520, 8923455937553017, 216095445904425947, 5233099961163002488, 126727881793625193513, 3068918844981224041565
Offset: 1

Views

Author

R. H. Hardin Apr 19 2011

Keywords

Comments

Column 3 of A189254

Examples

			Some solutions for 4X3
..3..5..1....1..2..4....3..0..2....1..3..5....4..2..1....1..4..5....1..0..5
..0..7..2....3..0..7....1..7..4....6..0..2....0..7..8....7..0..2....3..8..2
..6..4.10....6..5.11....6..5.11....9.11..4....3..6..5....3..9.11....9.11..4
..9..8.11....9.10..8....9.10..8....7..8.10...10..9.11...10..6..8....6..7.10
		

Formula

Empirical: a(n) = 20*a(n-1) +125*a(n-2) -566*a(n-3) +249*a(n-4) +916*a(n-5) -1703*a(n-6) +256*a(n-7) +691*a(n-8) -30*a(n-9) -9*a(n-10)

A189249 Number of n X 4 array permutations with each element making zero or one king moves.

Original entry on oeis.org

5, 1168, 76629, 7396009, 637586496, 56892084785, 5025023852501, 445205174822288, 39407984363284853, 3489215319159283593, 308912577758497124608, 27349797876932219710785, 2421416215254898335806661
Offset: 1

Views

Author

R. H. Hardin, Apr 19 2011

Keywords

Comments

Column 4 of A189254.

Examples

			Some solutions for 3 X 4
..5..4..7..2....4..1..2..3....5..2..1..3....0..6..7..3....1..4..3..2
..0.10..1..3....0..8..6.10....0..4.10.11....8..1.11..2....8..0.11..6
..8..9..6.11....5..9.11..7....9..8..7..6....9..4..5.10....5..9.10..7
		

Crossrefs

Cf. A189254.

Formula

Empirical: a(n) = 86*a(n-1) +773*a(n-2) -51741*a(n-3) +261147*a(n-4) +1858799*a(n-5) -7576930*a(n-6) -18369505*a(n-7) -63976305*a(n-8) +171881802*a(n-9) +1135450371*a(n-10) -543543057*a(n-11) -2342488484*a(n-12) -2204079757*a(n-13) +2422263217*a(n-14) +6125446560*a(n-15) -2843664887*a(n-16) -3962040267*a(n-17) +2834866226*a(n-18) -976262267*a(n-19) +196899773*a(n-20) +87195350*a(n-21) -15444135*a(n-22) -1459347*a(n-23) -867371*a(n-24) +86035*a(n-25) +10110*a(n-26) -675*a(n-27).

A189250 Number of nX5 array permutations with each element making zero or one king moves.

Original entry on oeis.org

8, 8448, 1818336, 637586496, 194762146816, 62111749014784, 19568579061640704, 6188469597764755456, 1954975627547701307392, 617793023145579401433088, 195210690041588272450666496, 61684603710077597393322917888
Offset: 1

Views

Author

R. H. Hardin Apr 19 2011

Keywords

Comments

Column 5 of A189254

Examples

			Some solutions for 3X5
..0..5..2..8..9....0..5..1..4..8....0..5..1..7..8....0..5..6..7..4
.10..1..3.13..4...10..7..2..3..9....6..2..3.14..4....1.12..2..3.13
..6..7.11.12.14....6.12.11.13.14...10.11.12.13..9...11.10..8.14..9
		

Formula

Empirical: a(n) = 306*a(n-1) +14084*a(n-2) -3413208*a(n-3) -37913760*a(n-4) +8041363520*a(n-5) +7688826048*a(n-6) -6889761706624*a(n-7) +5202653015808*a(n-8) +2802990333573632*a(n-9) +6790227351584768*a(n-10) -685857854458576896*a(n-11) -5372869001388253184*a(n-12) +116164522590448566272*a(n-13) +1256789003575108927488*a(n-14) -12036143805249992589312*a(n-15) -142057852914628144398336*a(n-16) +683316680811034016481280*a(n-17) +8712086151000102590218240*a(n-18) -20982360025136584182464512*a(n-19) -305170070109551820472844288*a(n-20) +390572789229382186934730752*a(n-21) +6546500740363863628181405696*a(n-22) -5637881394993849134168932352*a(n-23) -93018389080728146789938495488*a(n-24) +78010006763315815363184164864*a(n-25) +938532475978901353401761660928*a(n-26) -935967387951105246060341100544*a(n-27) -6982213489888968493175154933760*a(n-28) +8208536967855964007383840063488*a(n-29) +39282469839804826862212505141248*a(n-30) -49486474219645506705232888856576*a(n-31) -176989359286385376521393885151232*a(n-32) +218162101995909369906474371776512*a(n-33) +660664519366159029203710007836672*a(n-34) -807327523225250130720326915457024*a(n-35) -1854716951333209150350914899410944*a(n-36) +2438769433212246552233842789318656*a(n-37) +3459765062072259416271709299277824*a(n-38) -5166969359086050195655423057461248*a(n-39) -3804557769955258800724459934187520*a(n-40) +6687224973041483611579174526910464*a(n-41) +1954196501306439388375809209139200*a(n-42) -4445500346232178934795207645855744*a(n-43) -410453643009045559599373546946560*a(n-44) +769221483476061219363229324541952*a(n-45) +360532064443933187500208881139712*a(n-46) +441276677000374259250463602900992*a(n-47) -22984496745428881982229057634304*a(n-48) -86322375040741113884861240705024*a(n-49) -6338178283858655043956944928768*a(n-50) +2155843450859023408765146759168*a(n-51) +80416536594945518072280121344*a(n-52) -7344224354158872236340019200*a(n-53)

A189251 Number of nX6 array permutations with each element making zero or one king moves.

Original entry on oeis.org

13, 62272, 44308389, 56892084785, 62111749014784, 71437033921822425, 81032653651506521333, 92340416748367645903936, 105103003634568916624818957, 119678361478200246096700911625
Offset: 1

Views

Author

R. H. Hardin Apr 19 2011

Keywords

Comments

Column 6 of A189254

Examples

			Some solutions for 3X6
..0..1..2..8..3..4....0..1..2..8..3.11....0..1..2..8..3.11....0..1..2..8..4..5
..7.12.15..9..5.10....7.13.14..4..5.17....6.14.13.16..4..5....7.14..9..3.10.11
..6.13.14.16.11.17...12..6..9.15.16.10....7.12..9.10.15.17...12..6.13.15.17.16
		

A189252 Number of nX7 array permutations with each element making zero or one king moves.

Original entry on oeis.org

21, 456320, 1070959431, 5025023852501, 19568579061640704, 81032653651506521333, 330453235652954061843137, 1355117057188899341581651072, 5550437831744113835993347187363
Offset: 1

Views

Author

R. H. Hardin Apr 19 2011

Keywords

Comments

Column 7 of A189254

Examples

			Some solutions for 3X7
..0..1..2..9..3..4..5....0..1..2..9..3..4..5....0..1..2..9..3..4..5
.15.16.10.11.18.13..6...14..8.15.11.19.12..6...14.16..8.18.11..6.19
.14..7..8.17.12.19.20....7.16.17.10.18.13.20....7.15.10.17.12.20.13
		

A189253 Number of nX8 array permutations with each element making zero or one king moves.

Original entry on oeis.org

34, 3350016, 25950094568, 445205174822288, 6188469597764755456, 92340416748367645903936, 1355117057188899341581651072, 20019535342827950668977079681024, 295422965429980829725911541023975936
Offset: 1

Views

Author

R. H. Hardin Apr 19 2011

Keywords

Comments

Column 8 of A189254

Examples

			Some solutions for 3X8
..0..1..9..2..3..4..5..6....0..1..9..2..3..4..5..6....0..1..9..2..3..4..5..6
.17..8.19.11.12.13.22..7...16.10.18.12.19.21.23..7...16..8.11.12.21.20..7.14
.16.18.10.20.21.14.23.15...17..8.11.20.13.14.22.15...17.10.19.18.13.22.15.23
		

A189246 Number of n X n array permutations with each element making zero or one king moves.

Original entry on oeis.org

1, 24, 2961, 7396009, 194762146816, 71437033921822425, 330453235652954061843137, 20019535342827950668977079681024, 15708505438679657289806294970498013833233, 160414174990431372841568811126249791614409201147297
Offset: 1

Views

Author

R. H. Hardin, Apr 19 2011

Keywords

Examples

			Some solutions for 3 X 3:
..4..2..5....3..1..4....4..0..1....0..3..4....0..2..1....0..2..4....0..1..2
..0..1..7....0..2..7....3..7..2....1..8..2....4..8..7....6..7..1....6..8..5
..6..3..8....6..5..8....6..8..5....6..7..5....3..6..5....3..5..8....3..4..7
		

Crossrefs

Diagonal of A189254.

Extensions

a(9)-a(10) from Pontus von Brömssen, Sep 03 2024
Showing 1-8 of 8 results.