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.

A189604 Number of n X 3 array permutations with each element not moving, or moving one space E, S or NW.

Original entry on oeis.org

1, 6, 20, 72, 256, 912, 3248, 11568, 41200, 146736, 522608, 1861296, 6629104, 23609904, 84087920, 299483568, 1066626544, 3798846768, 13529793392, 48187073712, 171620807920, 611236571184, 2176951329392, 7753327130544
Offset: 1

Views

Author

R. H. Hardin, Apr 24 2011

Keywords

Comments

Column 3 of A189610.
Binomial transform of A006131 starting (1, 5, 9, 29, 65, ...). - Gary W. Adamson, Feb 19 2014

Examples

			Some solutions for 4 X 3:
.
   4  5  1    0  5  1    0  1  2    0  1  2
   0  3  2    7  4  2    3  4  5    3  4  5
   6  7  8    3  6  8    6 11  8   10  7  8
   9 10 11    9 10 11    9  7 10    6  9 11
.
   4  0  1    0  1  2    4  1  2
   7  3  2    3  8  5    0  3  5
  10 11  5    6  4  7    6  7  8
   6  9  8    9 10 11    9 10 11

Links

Crossrefs

Cf. A006131.

Programs

  • Mathematica
    a[n_] := Sum[Sum[4^j Binomial[k-j+1, j], {j, 0, Quotient[k+1, 2]}]* Binomial[n-1, k], {k, 0, n-1}];
a /@ Range[1, 24] (* Jean-François Alcover, Sep 24 2019, after Gary W. Adamson *)

Formula

Empirical: a(n) = 3*a(n-1) + 2*a(n-2).
G.f.: (x+3*x^2)/(1-3*x-2*x^2). - Vladimir Kruchinin, May 13 2011

A189605 Number of nX4 array permutations with each element not moving, or moving one space E, S or NW.

Original entry on oeis.org

1, 13, 72, 464, 2853, 17617, 108785, 671452, 4144996, 25586605, 157944449, 974979853, 6018479996, 37151644524, 229334423389, 1415664871777, 8738797243193, 53943965676260, 332992213004236, 2055536935944305
Offset: 1

Views

Author

R. H. Hardin Apr 24 2011

Keywords

Comments

Column 4 of A189610

Examples

			Some solutions for 3X4
..0..1..7..2....5..0..2..3....0..6..2..3....5..6..7..2....0..6..1..2
..4..5..6..3....4..1.11..6....9..1..5..7....0..1.11..3....9..5.11..3
..8..9.10.11....8..9.10..7....4..8.10.11....4..8..9.10....4..8.10..7

Links

Formula

Empirical: a(n) = 7*a(n-1) -3*a(n-2) -12*a(n-3) -11*a(n-4) +34*a(n-5) -27*a(n-6) +9*a(n-7) +7*a(n-8) +49*a(n-9) -82*a(n-10) +84*a(n-11) -54*a(n-12) +21*a(n-13) -6*a(n-14) +a(n-15)

A189606 Number of nX5 array permutations with each element not moving, or moving one space E, S or NW.

Original entry on oeis.org

1, 28, 256, 2853, 30283, 321815, 3414588, 36212912, 383990913, 4071436782, 43168209556, 457694879893, 4852734814404, 51451313282657, 545514314383676, 5783833141059232, 61323273361025444, 650181923557415105
Offset: 1

Views

Author

R. H. Hardin Apr 24 2011

Keywords

Comments

Column 5 of A189610

Examples

			Some solutions for 3X5
..6..0..2..3..4....0..7..8..2..3....0..7..2..3..4....0..1..2..3..4
.11..1..7.14..9....5..1.13.14..4....5..1.13.14..8...11..5..7..8..9
..5.10.12..8.13...10..6.11.12..9...10..6.11.12..9...10..6.12.13.14

Links

Formula

Empirical: a(n) = 13*a(n-1) -13*a(n-2) -128*a(n-3) -146*a(n-4) +1071*a(n-5) +769*a(n-6) -749*a(n-7) -2673*a(n-8) +3566*a(n-9) -13757*a(n-10) +7250*a(n-11) -4937*a(n-12) -1246*a(n-13) +3164*a(n-14) +189*a(n-15) -984*a(n-16) +566*a(n-17) +329*a(n-18) -189*a(n-19) +54*a(n-20) +27*a(n-21) for n>22

A189607 Number of nX6 array permutations with each element not moving, or moving one space E, S or NW.

Original entry on oeis.org

1, 60, 912, 17617, 321815, 5897476, 107793872, 1968061359, 35917517449, 655347656612, 11956214759290, 218119695889901, 3979116037755048, 72589531392230391, 1324217776135660990, 24157052394845982633
Offset: 1

Views

Author

R. H. Hardin Apr 24 2011

Keywords

Comments

Column 6 of A189610

Examples

			Some solutions for 3X6
..0..8..2.10..3..5....0..1..2..3.11..5....0..1..9..3.11..4....0..1..2.10.11..4
..6..1.15..9..4.11....6..7.15..9..4.10...13..6..2..8.10..5....6.14..8..3..9..5
.12..7.13.14.16.17...12.13..8.14.16.17...12..7.14.15.16.17...12..7.13.15.16.17

Links

Formula

Empirical: a(n) = 27*a(n-1) -127*a(n-2) -740*a(n-3) +747*a(n-4) +34995*a(n-5) -5506*a(n-6) -248292*a(n-7) -1174016*a(n-8) +1007958*a(n-9) -6861339*a(n-10) +41430256*a(n-11) +51611008*a(n-12) +198872876*a(n-13) -868258957*a(n-14) +1605556233*a(n-15) -7531204340*a(n-16) +1848561932*a(n-17) +6186956818*a(n-18) -4662718722*a(n-19) +45191482278*a(n-20) +97124216354*a(n-21) -55135475594*a(n-22) -27287536597*a(n-23) -171514334842*a(n-24) -726729691066*a(n-25) -629428131178*a(n-26) +173178060771*a(n-27) +427006220020*a(n-28) +2317766584100*a(n-29) +4411572299192*a(n-30) +3018492633598*a(n-31) -49374942909*a(n-32) -3044087792460*a(n-33) -10242069320303*a(n-34) -13737406955417*a(n-35) -8647612812832*a(n-36) -447720866054*a(n-37) +8671998792069*a(n-38) +20571483610312*a(n-39) +21760073504185*a(n-40) +12564766054592*a(n-41) -39461914321*a(n-42) -12111944579432*a(n-43) -21521945563638*a(n-44) -18557201154461*a(n-45) -9762845716612*a(n-46) +1789973055064*a(n-47) +9250208603329*a(n-48) +12844537868975*a(n-49) +9355142418757*a(n-50) +4273826939521*a(n-51) -1198279677480*a(n-52) -3756392714910*a(n-53) -4341134125770*a(n-54) -2896130615108*a(n-55) -1279535523194*a(n-56) +117809240013*a(n-57) +724830885103*a(n-58) +833606712872*a(n-59) +593545615487*a(n-60) +315058164501*a(n-61) +91626028809*a(n-62) -22707962227*a(n-63) -62984709313*a(n-64) -59302149654*a(n-65) -42411923185*a(n-66) -25348175173*a(n-67) -13452835237*a(n-68) -6385446334*a(n-69) -2765569003*a(n-70) -1092490969*a(n-71) -398969847*a(n-72) -133968639*a(n-73) -41534265*a(n-74) -11796130*a(n-75) -3102673*a(n-76) -750560*a(n-77) -165926*a(n-78) -32497*a(n-79) -5745*a(n-80) -925*a(n-81) -136*a(n-82) -15*a(n-83) -a(n-84) for n>85

A189608 Number of nX7 array permutations with each element not moving, or moving one space E, S or NW.

Original entry on oeis.org

1, 129, 3248, 108785, 3414588, 107793872, 3394457868, 106717857552, 3352763054744, 105288130659056, 3305643786649888, 103772022994114688, 3257440136563770512, 102248757981895108688, 3209460671164514648880
Offset: 1

Views

Author

R. H. Hardin Apr 24 2011

Keywords

Comments

Column 7 of A189610

Examples

			Some solutions for 3X7
..0..1..2..3..4..5..6....0..1.10..2.12..4..6....0..1..2.11..4.13..6
.15..8..9.18.11.20.12....7.16..8..3.11..5.13....7..8.17..3.10..5.12
..7.14.16.10.17.19.13...14.15..9.17.18.19.20...14.15..9.16.18.19.20

Links

A189609 Number of n X 8 array permutations with each element not moving, or moving one space E, S or NW.

Original entry on oeis.org

1, 277, 11568, 671452, 36212912, 1968061359, 106717857552, 5778059258273, 312573095738121, 16898643737922425, 913264073225048477, 49345410349072594251, 2665888554266786412238, 144014204839657901069783
Offset: 1

Views

Author

R. H. Hardin, Apr 24 2011

Keywords

Comments

Column 8 of A189610.

Examples

			Some solutions for 3 X 8
..9..0..2.12..4..5..6..7....9..0..2.12.13.14..5..7....0..1.11.12..3..5.15..6
.17..1.19..3.11.22.13.15...17..1.10..3..4.22..6.15....8..9..2.10..4.13.14..7
..8.16.10.18.20.21.14.23....8.16.18.11.19.20.21.23...16.17.18.19.20.21.22.23

Links

Crossrefs

Cf. A189610.

A189603 Number of n X n array permutations with each element not moving, or moving one space E, S or NW.

Original entry on oeis.org

1, 3, 20, 464, 30283, 5897476, 3394457868, 5778059258273, 29117129479453520, 434446215594380010575
Offset: 1

Views

Author

R. H. Hardin, Apr 24 2011

Keywords

Comments

Diagonal of A189610.

Examples

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

Crossrefs

Cf. A189610.
Showing 1-7 of 7 results.

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