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 1-3 of 3 results.

A304133 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3 or 6 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 3, 5, 3, 5, 7, 7, 5, 8, 17, 9, 17, 8, 13, 31, 19, 19, 31, 13, 21, 49, 33, 44, 33, 49, 21, 34, 103, 53, 80, 80, 53, 103, 34, 55, 193, 89, 140, 176, 140, 89, 193, 55, 89, 327, 155, 244, 320, 320, 244, 155, 327, 89, 144, 641, 261, 436, 582, 651, 582, 436, 261, 641, 144
Offset: 1

Views

Author

R. H. Hardin, May 07 2018

Keywords

Comments

Table starts
..1...2...3...5....8...13....21....34....55.....89....144.....233.....377
..2...5...7..17...31...49...103...193...327....641...1207....2129....4039
..3...7...9..19...33...53....89...155...261....439....749....1271....2149
..5..17..19..44...80..140...244...436...800...1444...2584....4630....8328
..8..31..33..80..176..320...582..1112..2178...4222...8066...15568...30220
.13..49..53.140..320..651..1321..2673..5293..10668..21704...43407...86685
.21.103..89.244..582.1321..2945..6333.13315..28932..63006..134021..284831
.34.193.155.436.1112.2673..6333.14708.33148..76987.180185..411855..940653
.55.327.261.800.2178.5293.13315.33148.79188.192201.476031.1166023.2823979

Examples

			Some solutions for n=5 k=4
..0..0..1..1. .0..0..1..1. .0..1..1..1. .0..1..1..0. .0..0..1..1
..0..0..0..1. .0..0..0..1. .0..0..1..1. .1..1..1..1. .0..0..0..1
..0..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1. .0..1..1..1
..0..0..1..1. .0..0..0..0. .0..1..1..1. .1..1..1..0. .0..0..1..1
..0..0..0..1. .0..0..0..0. .0..0..1..1. .1..1..0..0. .0..0..0..1

Links

Crossrefs

Column 1 is A000045(n+1).
Column 2 is A303677.

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = a(n-1) +4*a(n-3) -2*a(n-4) for n>5
k=3: a(n) = a(n-1) +2*a(n-3) for n>7
k=4: a(n) = a(n-1) +3*a(n-3) +a(n-5) -a(n-6) -5*a(n-7) -2*a(n-8) +2*a(n-10) for n>13
k=5: [order 16] for n>22
k=6: [order 45] for n>48
k=7: [order 79] for n>87

A304221 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 3, 5, 3, 5, 7, 7, 5, 8, 17, 10, 17, 8, 13, 31, 17, 17, 31, 13, 21, 49, 32, 32, 32, 49, 21, 34, 103, 56, 62, 62, 56, 103, 34, 55, 193, 93, 108, 141, 108, 93, 193, 55, 89, 327, 159, 190, 279, 279, 190, 159, 327, 89, 144, 641, 279, 348, 509, 740, 509, 348, 279, 641, 144
Offset: 1

Views

Author

R. H. Hardin, May 08 2018

Keywords

Comments

Table starts
..1...2...3...5....8...13....21.....34.....55......89.....144......233......377
..2...5...7..17...31...49...103....193....327.....641....1207.....2129.....4039
..3...7..10..17...32...56....93....159....279.....484.....829.....1426.....2468
..5..17..17..32...62..108...190....348....636....1152....2082.....3768.....6840
..8..31..32..62..141..279...509....996...1951....3730....7226....14057....27115
.13..49..56.108..279..740..1628...3759...9029...20849...48072...112793...263016
.21.103..93.190..509.1628..4263..11307..32315...89108..241808...671482..1860876
.34.193.159.348..996.3759.11307..33924.112860..357754.1104388..3529160.11247788
.55.327.279.636.1951.9029.32315.112860.451917.1714008.6230016.23602199.89500014

Examples

			Some solutions for n=7 k=4
..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..1..1..1. .0..0..1..1
..0..0..0..0. .0..1..1..1. .0..0..0..0. .0..0..1..1. .0..1..1..1
..0..0..0..0. .1..1..1..1. .0..0..1..0. .0..0..0..1. .1..1..1..1
..0..0..0..0. .1..1..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1
..0..0..1..0. .1..1..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1
..0..0..0..0. .1..1..0..1. .0..0..0..0. .0..0..0..0. .1..1..1..1
..0..0..0..0. .1..1..1..1. .0..0..0..0. .1..0..0..0. .0..1..1..0

Links

Crossrefs

Column 1 is A000045(n+1).
Column 2 is A303677.

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = a(n-1) +4*a(n-3) -2*a(n-4) for n>5
k=3: a(n) = a(n-1) +a(n-3) +2*a(n-4) for n>5
k=4: a(n) = a(n-1) +2*a(n-3) +a(n-4) +a(n-5) -2*a(n-7) for n>9
k=5: a(n) = a(n-1) +3*a(n-3) +a(n-4) +a(n-6) -2*a(n-7) -a(n-10) for n>14
k=6: [order 14] for n>19
k=7: [order 18] for n>24

A305482 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 6 or 8 king-move adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 3, 5, 3, 5, 7, 7, 5, 8, 17, 10, 17, 8, 13, 31, 21, 21, 31, 13, 21, 49, 40, 48, 40, 49, 21, 34, 103, 70, 98, 98, 70, 103, 34, 55, 193, 125, 192, 277, 192, 125, 193, 55, 89, 327, 231, 368, 577, 577, 368, 231, 327, 89, 144, 641, 419, 732, 1245, 1558, 1245, 732, 419, 641
Offset: 1

Views

Author

R. H. Hardin, Jun 02 2018

Keywords

Comments

Table starts
..1...2...3....5....8....13.....21.....34......55......89......144.......233
..2...5...7...17...31....49....103....193.....327.....641.....1207......2129
..3...7..10...21...40....70....125....231.....419.....752.....1365......2482
..5..17..21...48...98...192....368....732....1480....2932.....5776.....11486
..8..31..40...98..277...577...1245...2868....6381...14206....31630.....70391
.13..49..70..192..577..1558...3910..10465...27679...70960...185085....482009
.21.103.125..368.1245..3910..11438..34687..106558..317866...952180...2866802
.34.193.231..732.2868.10465..34687.123104..440388.1501195..5216253..18221847
.55.327.419.1480.6381.27679.106558.440388.1894686.7620015.31132355.129187191

Examples

			Some solutions for n=5 k=4
..0..0..0..0. .0..1..1..1. .0..1..1..1. .0..0..0..1. .0..0..0..0
..0..0..0..0. .0..0..1..1. .1..1..1..1. .0..0..0..0. .1..0..0..0
..0..0..1..0. .0..0..0..1. .1..1..1..1. .0..0..0..0. .1..1..0..0
..1..0..1..1. .0..0..0..0. .0..1..1..1. .0..1..0..0. .0..0..0..0
..1..1..1..1. .1..0..0..0. .0..0..1..1. .1..1..0..1. .1..0..0..0

Links

Crossrefs

Column 1 is A000045(n+1).
Column 2 is A303677.

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = a(n-1) +4*a(n-3) -2*a(n-4) for n>5
k=3: a(n) = a(n-1) +3*a(n-3) -2*a(n-6) for n>9
k=4: [order 10] for n>13
k=5: [order 29] for n>33
k=6: [order 60] for n>66
Showing 1-3 of 3 results.

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